Machine-learning-assisted side-channel analysis (ML-assisted SCA) automates the procedure of analyzing side-channel activities to reconstruct secrets. Although ML-assisted SCA does produce promising results, it is hard to determine whether its machine-learning model tends to reconstruct secrets or generate new instances. In this paper, we revisit the first general ML-assisted SCA framework for media software (Yuan et al. USENIX Security 2022), which we refer to as the Manifold-SCA framework, with a case study of reconstructing images from cache activities. We show that Manifold-SCA tends to generate images more than reconstruct them. Inspired by the autoencoder implemented in the Manifold-SCA framework, we theoretically and experimentally show that an autoencoder is sufficient to reconstruct images from cache activities. Through three ablation studies, we show that an autoencoder outperforms the Manifold-SCA framework under all scenarios. In the end, we apply an autoencoder to analyze practical cache activities collected by a profiling-based Prime+Probe attack, and show that an autoencoder can reconstruct partial pixel-related activities, but these activities are insufficient to reconstruct images due to the information loss in the activities.

In this paper, we first propose a new design strategy of 2D Z-complementary array quads (2D-ZCAQs) with feasible array sizes. A 2D-ZCAQ consists of four distinct unimodular arrays satisfying zero 2D auto-correlation sums for non-trivial 2D time-shifts within certain zone. Then, we obtain the upper bounds on the column sequence peak-to-mean envelope power ratio (PMEPR) of the constructed 2D-ZCAQs by using specific auto-correlation properties of some seed sequences. The constructed 2D-ZCAQs with bounded column sequence PMEPR can be used as a potential alternative to 2D Golay complementary array sets for practical applications.

In [3], the relation between stabilizer codes and binary codes over the symplectic inner product and symplectic weight was established. In the current work, we present a relation between the symplectic weight and symbol-pair weight and use it to construct stabilizer codes of length n from binary codes of length n defined over the symbol-pair metric and Euclidean inner product. In particular, we use certain length n binary LCD codes over the symbol-pair metric to obtain stabilizer codes of length n. We also present the Modified CSS construction which outperforms the CSS construction in the given setup.

Zero correlation zone (ZCZ) sequence sets play an important role in interference-free quasi-synchronous code-division multiple access communications. In this paper, for the first time, we investigate the periodic correlation properties of polyphase sequences obtained from paraunitary (PU) matrices, which shows the inherent relationship between PU matrix and ZCZ sequence sets. Our investigation suggests that any arbitrary PU matrix can produce ZCZ sequence sets by controlling its expanded form. The key idea is to impose certain restrictions on the expanded forms of the PU matrices to enable precise computation of the periodic correlation functions of the constructed sequences. We show that our proposed construction leads to near-optimal ZCZ sequence sets with regard to the ZCZ set size upper bound.

The region of interest (ROI) of medical images in content-based image retrieval (CBIR) systems often require content authentication and verification. This is because adversarial modification of the stored image could have lethal effect on research, diagnostic outcome and the outcome of some forensic investigations. In this work, both robust watermarking and Fragile Steganography were combined with image search features to design a medical image retrieval system that incorporates ROI integrity verification. Original ROI features were pre-computed and embedded into archival images and utilised during retrieval for image integrity checks. The average global image PSNR was 38.36dB while the ROI PSNR was maintained at an average of 46dB with all watermark search features retrieved at zero bit error rate (BER) provided the attack on the image is not perceptible.

In this paper, we revisit the problem of finding the longest systematic-length k for a linear minimum storage regenerating (MSR) code with optimal repair of only systematic part, for a given per-node storage capacity l and an arbitrary number of parity nodes r. We study the problem by following a geometric analysis of linear subspaces and operators. First, a simple quadratic bound is given, which implies that k = r + 2 is the largest number of systematic nodes in the scalar scenario. Second, an r-based-log bound is derived, which is superior to the upper bound on log-base 2 in the prior work. Finally, an explicit upper bound depending on the value of r2/l is introduced, which further extends the corresponding result in the literature.

In this paper, binary decision diagram (BDD)-based dual-rail precharge logic circuit schemes have been developed to counter differential power analysis attacks, timing attacks, and early propagation attacks. Different precharge logic schemes (top precharging, top-bottom precharging, bottom precharging, and symmetric nMOS bottom precharging) are presented and evaluated. The hallmark of our circuit schemes is that an identical number of switchings is ensured on each circuit path. The transistors are interconnected to create pull-up and pull-down paths to outputs by way of binary decisions based on the input variables, so as to realize the required Boolean function. A simple synthesis algorithm for mapping a given Boolean function to such a BDD-based circuit is also presented. Experimentation has been carried out on two 4-, 16-, 32-, and 64-bits S-boxes to establish resistance of our circuits to power analysis attack and to highlight the low-power characteristics with the help of attributes such as peak power variance, average power, propagation delay, normalized standard deviation of power, and normalized energy deviation. Differential power attacks such as difference of mean and correlation power analysis have been carried out. Resilience to the early propagation effect is also demonstrated.

We investigate spectrally-constrained sequences (SCSs), which are applicable to the communication and radar systems operating over non-contiguous carriers or frequency slots. Typical examples of such systems are overlay cognitive radio or cognitive radar networks. First, we derive the periodic- and aperiodic-correlation lower bounds for single-channel SCSs and multi-channel SCSs by convex optimization in the frequency domain. Each of these bounds reduces to a Welch bound when the number of forbidden carriers is set to zero. We then propose systematic constructions of optimal unimodular single-channel SCSs with the aid of cyclic difference sets and the theory of maximal-length shift register sequences.

Sequences with low correlation have important applications in communications, radar, and cryptography. In this paper, a simple construction of polyphase sequences using additive and multiplicative characters over the finite field Fqis proposed. The construction works for any finite field Fqwith q > 2 and generates a family of q - 1 sequences with period q - 1 and maximum correlation √q. This family is asymptotically optimal with respect to the well-known Welch bound. Most notably, the maximum autocorrelation magnitude of each sequence in this family is equal to 1, and every two distinct sequences are orthogonal to each other. The distribution of the correlation magnitudes of this family is also established.

Stepped frequency radar technology, where the transmit waveform consists of a sequence of tones, has long been suggested for cost-effective and high-resolution applications. One recent use of this technology is in automotive application where, in addition to cost-effectiveness, a random stepped frequency (RSF) waveform can significantly reduce the interference between vehicles. In this paper we provide a generic framework for the range and Doppler measurements for multiple targets. We further suggest two possible methods for reducing the computational complexity of RSF waveforms processing, which is important for future automotive applications.

In this paper, we revisit the problem of characterizing the secrecy capacity of minimum storage regenerating (MSR) codes under the passive (l1, l2)-eavesdropper model, where the eavesdropper has access to data stored on l1nodes and the repair data for an additional l2nodes. We study it from the informationtheoretic perspective. First, some general properties of MSR codes as well as a simple and generally applicable upper bound on secrecy capacity are given. Second, a new concept of stable MSR codes is introduced, where the stable property is shown to be closely linked with secrecy capacity. Finally, a comprehensive and explicit result on secrecy capacity in the linear MSR scenario is present, which generalizes all related works in the literature and also predicts certain results for some unexplored linear MSR codes.

Non-malleability is an important and intensively studied security notion for many cryptographic primitives. In the context of public key encryption, this notion means it is infeasible for an adversary to transform an encryption of some message m into one of a related message m' under the given public key. Although it has provided a strong security property for many applications, it still does not suffice for some scenarios like the system where the users could issue keys on-the-fly. In such settings, the adversary may have the power to transform the given public key and the ciphertext. To withstand such attacks, Fischlin introduced a stronger notion, known as complete non-malleability, which requires that the non-malleability property be preserved even for the adversaries attempting to produce a ciphertext of some related message under the transformed public key. To date, many schemes satisfying this stronger security have been proposed, but they are either inefficient or proved secure in the random oracle model. In this work, we put forward a new encryption scheme in the common reference string model. Based on the standard DBDH assumption, the proposed scheme is proved completely non-malleable secure against adaptive chosen ciphertext attacks in the standard model. In our scheme, the well-formed public keys and ciphertexts could be publicly recognized without drawing support from unwieldy techniques like non-interactive zero knowledge proofs or one-time signatures, thus achieving a better performance.

Here, we revisit the problem of exploring the secrecy capacity of minimum storage cooperative regenerating (MSCR) codes under the (l2 l2)-eavesdropper model, where the eavesdropper can observe the data stored on l1nodes and the repair downloads of an additional l2nodes. Compared to minimum storage regenerating (MSR) codes which support only single node repairs, MSCR codes allow efficient simultaneous repairs of multiple failed nodes, referred to as a repair group. However, the repair data sent from a helper node to another failed node may vary with different repair groups or the sets of helper nodes, which would inevitably leak more data information to the eavesdropper and even render the storage system unable to maintain any data secrecy. In this paper, we introduce and study a special category of MSCR codes, termed “stable” MSCR codes, where the repair data from any one helper node to any one failed node is required to be independent of the repair group or the set of helper nodes. Our main contributions include: 1) Demonstrating that two existing MSCR codes inherently are not stable and thus have poor secrecy capacity; 2) Converting one existing MSCR code to a stable one, which offers better secrecy capacity when compared to the original one; and 3) Employing information theoretic analysis to characterize the secrecy capacity of stable MSCR codes in certain situations.

A sequence is said to be spectrally-constrained if it has to satisfy a spectral map consisting of several non-contiguous nulled frequency-slots. Such sequences play a key role in emerging spectrally-constrained systems such as cognitive radio and cognitive radar. In this paper, we study two types of spectrally-constrained sequences (SCSs), one with low periodic auto-correlation function (PACF) sidelobe, the other with zero auto-correlation zone (ZACZ). By deriving a correlation lower bound, we show that Type-I SCSs are optimal with minimum total PACF sidelobe energy provided that uniform power allocation is applied to all active (non-nulled) frequency-slots. We also propose optimal Type-II SCSs, each having maximum ZACZ width, for certain spectral map patterns.

In this paper, we present a generic framework for constructing systematic minimum storage regenerating codes with two parity nodes based on the invariant subspace technique. Codes constructed in our framework not only contain some best known codes as special cases, but also include some new codes with key properties, such as the optimal access property and the optimal update property. In particular, for a given storage capacity of an individual node, one of the new codes has the largest number of systematic nodes and two of the new codes have the largest number of systematic nodes with the optimal update property.

In this paper, we present a direct construction of zero-correlation zone (ZCZ) sequence sets (each associated with a graph) from the second order cosets of the first-order generalized Reed-Muller codes. This settles an open problem introduced by Rathinakumar and Chaturvedi in their 2008 paper.

For an even-period binary Z-complementary pair (EB-ZCP), if it is not a Golay complementary pair (GCP), we show that Z ≤ N-2, where N and Z denote the sequence length and the zero correlation zone (ZCZ) width, respectively. This result partially answers the Fan-Yuan-Tu conjecture in 2007. In addition, we present a construction of EB-ZCPs with large ZCZ widths, where N=2m+1+2mand Z=2m+1. Interestingly, each of the proposed EB-ZCPs features zero out-of-phase aperiodic auto-correlation sums except for the time-shift of ±2m+1, thus displaying a very close correlation property to that of GCPs.

Owing to the zero non-trivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multi-carrier code-division multiple-access (MC-CDMA) communications in order to provide zero interference performance. When each complementary code is arranged to be a matrix, the peak-to-mean envelope power ratio (PMEPR) of the CCC-MC-CDMA system is determined by the column sequences of the complementary matrices. The existing CCC have the column sequence PMEPR of M, where M denotes the number of subcarriers in a CCC-MC-CDMA system. In practice, M is generally large and a PMEPR approaching this value is unacceptable. To solve this problem, a new class of CCC using generalized Boolean functions and with a column sequence PMEPR of at most 2 is proposed in this paper.

A pair of sequences is called a Golay complementary pair (GCP) if their aperiodic autocorrelation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 2α10β26γ(where \(α, β, γ) are nonnegative integers). To fill the gap left by the odd-lengths, we investigate the optimal odd-length binary (OB) pairs, which display the closest correlation property to that of GCPs. Our criteria of closeness is that each pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic autocorrelation sums. Such optimal pairs are called optimal OB Z-complementary pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N+1)/2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications, where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families, which are useful in studying partially balanced incomplete block design.

The Levenshtein bound on aperiodic correlation, which is a function of the weight vector, is tighter than the Welch bound for sequence sets over the complex roots of unity when$M\geq 4$and$n\geq 2$, where$M$denotes the set size and$n$the sequence length. Although it is known that the tightest Levenshtein bound is equal to the Welch bound for$M\in\{1,2\}$, it is unknown whether the Levenshtein bound can be tightened for$M=3$, and Levenshtein, in his paper published in 1999, postulated that the answer may be negative. A new weight vector is proposed in this paper, which leads to a tighter Levenshtein bound for$M=3$,$n\geq 3$and$M\geq 4$,$n\geq 2$. In addition, the explicit form of the weight vector (which is derived by relating the quadratic minimization to the Chebyshev polynomials of the second kind) in Levenshtein's paper is given. Interestingly, this weight vector also yields a tighter Levenshtein bound for$M=3$,$n\geq 3$and$M\geq 4$,$n\geq\sqrt{M}$, a fact not noticed by Levenshtein.

In this paper we introduce the optimal odd-period binary Z-complementary pairs (OB-ZCPs), which display properties similar to Golay complementary pairs. These pairs have the maximum possible zero-correlation-zone (ZCZ) of width (N + 1)/2, where N denotes the sequence length, and the minimum possible magnitude of 2 for each out-of-zone aperiodic auto-correlation sum. Furthermore, we show that the optimal OB-ZCPs correspond to sets of almost difference families and present some of their interesting properties.

The Levenshtein bound, as a function of the weight vector, is only known to be tighter than the Welch bound on aperiodic correlation for K ≥ 4, N ≥ 2, where K and N denoting the set size and the sequence length, respectively. A quadratic weight vector is proposed in this paper which leads to a tighter Levenshtein bound for K ≥ 4, N ≥ 2 and K = 3, N ≥ 4. The latter case was left open by Levensthein.

In this paper, we revisit a method to produce binary sequences using the most significant bit map fromZ4to the binary field. This method is useful for the construction of binary sequences with low correlation and large family size. There may be more cases where starting withZ4could help researchers design new low correlation sequences for code-division multiple access application.

The volume of time series data grows rapidly in various applications such as network traffic management, telecommunications, finance and sensor network. To reduce the cost of storage, transmission and processing of time series data, the need for more compact representations of time series data is compelling. Segmentation is one of the most commonly used methods to meet this requirement. Both PLA and PPA are common segmentation methods which divide a time series into segments and use a linear function or a polynomial function to approximate each segment, respectively. However, while most of the current PLA and PPA methods aim to minimize the holistic error between the approximation and the original time series, few works try to represent time series as compact as possible with an error bound guarantee on each data point. Furthermore, in many real world situations, the patterns of the time series do not follow a constant rule such that using only one type of functions may not yield the best compaction.

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. With the increasingly crowded electromagnetic spectrum, interference between different systems is becoming more important. In this paper, we consider the Low Probability of Intercept properties of some commonly used sequence families, with respect to their triple correlation function. The binary families we consider include the Gold sequence family, the Gold-like sequence family with quadratic span, and the Bent Function sequence family.

In this paper, the partial Hamming correlation properties of frequency-hopping sequences (FHSs) are discussed. The Peng-Fan bounds on sets of FHSs are generalized to the case of partial correlation. Both individual FHSs with optimal partial autocorrelation and sets of FHSs with optimal partial correlation are presented. The former has more new parameters compared with the known individual FHSs with optimal partial autocorrelation, while the later is obtained in the literature for the first time.

In this paper, an upper bound for a hybrid incomplete exponential sum over finite fields is derived. This bound is then used to obtain lower and upper bounds for aperiodic Hamming correlation of frequency-hopping sequences based on power functions.

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. Perfect autocorrelation sequences are however very rare. We recall a technique that yields examples of nonbinary sequences with perfect autocorrelation over enlarged PSK (PSK+) alphabets. It turns out that there are a large number of existing sequence constructions that we can utilize yield perfect correlation sequences, and that this affords a large number of choices for the length and alphabet of such sequences. We have also considered sequences with ideal autocorrelation with respect to their LPI/LPD properties and obtained initial results in this direction.

In this paper, we derive a new bound on maximum nontrivial Hamming correlation of frequency hopping (FH) sequences from the Singleton bound in error correcting code literature, and we discuss the relation between the new bound and the known ones on FH sequences. Further, we construct two classes of FH sequences from punctured Reed–Solomon codes and one class of FH sequences from polynomial functions, which meet the new bound.

In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employingd-form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets usingm-sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriated-form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets.

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. Perfect autocorrelation sequences are however exceedingly rare. We discuss a technique that yields examples of such designs over enlarged PSK (PSK+) alphabets. We also design nearly perfect autocorrelation sequences over enlarged QAM (QAM+) alphabets, compatible with contemporary wireless transmission standards.

In this paper we revisit a method to produce binary sequences using a non-linear polynomial mapping from Z4to the binary field. This method is useful to construct binary sequences with low correlation with large sizes. We conclude that Z4may be the best starting ring to generate large binary families for code-division multiple access (CDMA) application.

This paper presents new families of two and three-dimensional arrays designed for watermarking. The array construction is algebraic, based on finite fields. The arrays have good auto and cross-correlation with other family members. The family size is large enough to be used in watermarking at the point of origin, providing a unique watermark for every video and image. Such watermarks have applications in surveillance, sub-image object tracking and as fingerprints for proof of tampering, audit trail monitoring and traitor tracing.

In this paper, we are concerned with Hadamard matrices with a certain noncyclic property. First we show that when the first column of a Sylvester Hadamard matrix of order 2m, m ≥ 2, a positive integer, is removed, the number of shift distinct row vectors in the matrix is given by 2m-m. Then, for m ≥ 4, we construct an infinite family of Hadamard matrices with a property that when the first column of the Hadamard matrix is removed, all the row vectors of the matrix are shift distinct. These Hadamard matrices are useful in constructing low correlation zone sequences.

Variable-weight Optical orthogonal code (OOC) was introduced by G-C Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirement. In this paper, a construction for optimal variable-weight OOCs via cyclic difference families is given. Several new constructions for cyclic difference families are also given. By using these constructions, new optimal (n,W, 1,Q)-OOCs for 2 ≤ |W| ≤ 4 are constructed.

The authors describe signature constructions in the standard model based on the hardness of the computational Diffie–Hellman problem over gap and co-gap groups. The schemes are computationally efficient and have reduced public parameter size when compared with other identity-based signatures in the standard model.

There is significant interest in the data mining and network management communities about the need to improve existing techniques for clustering multivariate network traffic flow records so that we can quickly infer underlying traffic patterns. In this paper, we investigate the use of clustering techniques to identify interesting traffic patterns from network traffic data in an efficient manner. We develop a framework to deal with mixed type attributes including numerical, categorical, and hierarchical attributes for a one-pass hierarchical clustering algorithm. We demonstrate the improved accuracy and efficiency of our approach in comparison to previous work on clustering network traffic.

The capability of an employee to violate the policy of an organization is a concern for an employer. Monitoring is a measure taken by an employer to discourage an employee from acting inappropriately. However, current monitoring techniques tend to raise privacy issues because they violate the privacy rights of employees. Applying a monitoring technique without violating the privacy of employees is the aim of this paper. We propose a design and a protocol which give an employer the opportunity to monitor employee email in order to detect company policy violations. This can be achieved without violating the privacy of honest employees, while at the same time revealing evidence about the illegal actions of dishonest employees.

In this note, by using a modification of the families B and C, we obtain a larger family of optimal quadriphase sequences, D over Z4. In contrast to the families B and C, the family D has the same length and the same maximal nontrival correlation value, but with double the size

In this correspondence, we present a family of binary 2nsequences of period 2(2n-1) where n is an integer, which can be seen as a generalization of nonlinear binary sequences obtained from Z4sequences and recently constructed GKW (Gold, Kasami, and Welch)-like sequences. The sequences have low correlations and are useful in code-division multiple-access (CDMA) communication systems and cryptography

In this paper we construct families of low correlation zone (LCZ) sequences derived from interleaved technique and Hadamard matrices. These sequences are useful in certain quasi-synchronous code-division multiple access (QS-CDMA) communication systems

The theory of algebraic-geometric codes with respect to the Hamming metric has been well developed. However, in many applications where non-binary signals are transmitted or stored the Lee metric is a more appropriate metric than the Hamming metric. In our previous work, we presented a polynomial-time Lee-metric decoding algorithm for algebraic-geometricable codes. Our algorithm generalizes the interpolation-based Lee-metric decoding algorithm for Reed-Solomon codes in the literature. In this paper, we derive an explicit upper bound on the Lee-error correcting radius of our decoding algorithm. The bound also applies to the Lee-metric Reed-Solomon decoding. As far as we know no such explicit bound is available in the literature.

In this correspondence, we present a new family of nonbinary sequences with three-level nontrivial correlations and large linear complexity. The sequences may be considered as nonlinear analogues of the well-known sequences by Trachtenberg and Helleseth. It is shown that the family is optimal with respect to the Welch bound in terms of root mean square of all nontrivial correlations. We also determine the correlation distribution of the new family.

Let F/sub q/[X/sub 1/,...,X/sub m/] denote the set of polynomials over F/sub q/ in m variables, and F/sub q/[X/sub 1/,...,X/sub m/]/sub /spl les/u/ denote the subset that consists of the polynomials of total degree at most u. Let H(T) be a nontrivial polynomial in T with coefficients in F/sub q/[X/sub 1/,...,X/sub m/]. A crucial step in interpolation-based list decoding of q-ary Reed-Muller (RM) codes is finding the roots of H(T) in F/sub q/[X/sub 1/,...,X/sub m/]/sub /spl les/u/. In this correspondence, we present an efficient root-finding algorithm, which finds all the roots of H(T) in F/sub q/[X/sub 1/,...,X/sub m/]/sub /spl les/u/. The algorithm can be used to speed up the list decoding of RM codes.

This paper presents the generalized Udaya Sidiqi sequences which are the interleaved version of Gold like binary sequences of period satisfying the Welch bound maximum out of phase correlations. The sequences have large linear complexity and low correlations and are useful in code division multiple access (CDMA) communication systems and cryptography. A direct method to compute the correlation using the trace sequence representation and a sequence from a quadratic form are presented.

This paper describes the algebraic-geometric (AG) codes for the Lee metric and derives a lower bound for the minimum Lee distance of AG codes. A Lee-metric decoding algorithm for AG codes is also discussed. This algorithm gives a performance-complexity, which achieves an error-correcting capability.

We demonstrate that many well-known binary, quaternary, and q-ary codes are cocyclic Hadamard codes; that is, derived from a cocyclic generalized Hadamard matrix or its equivalents. Nonlinear cocyclic Hadamard codes meet the generalized Plotkin bound. Using presemifield multiplication cocycles, we construct new equivalence classes of cocyclic Hadamard codes which meet the Plotkin bound.

We introduce linear cyclic codes over the ring F/sub 2/+uF/sub 2/={0,1,u,u~=u+1}, where u/sup 2/=0 and study them by analogy with the Z/sub 4/ case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z/sub 4/-codes. Unlike the Z/sub 4/ case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-dual codes through a linear Gray map.

We give a simple decoding algorithm to decode linear cyclic codes of odd length over the ring R=F/sub 2/+uF/sub 2/={0,1,u,u~=u+1}, where u/sup 2/=0. A spectral representation of the cyclic codes over R is given and a BCH-like bound is given for the Lee distance of the codes. The ring R shares many properties of Z/sub 4/ and F/sub 4/ and admits a linear "Gray map".

We construct new sequences over finite rings having optimal Hamming correlation properties. These sequences are useful in frequency hopping multiple-access (FHMA) spread-spectrum communication systems. Our constructions can be classified into linear and nonlinear categories, both giving optimal Hamming correlations according to Lempel-Greenberger (1974) bound. The nonlinear sequences have large linear complexity and can be seen as a generalized version of GMW sequences over fields.

New families of biphase sequences of size 2/sup r-1/+1, r being a positive integer, are derived from families of interleaved maximal-length sequences over Z/sub 4/ of period 2(2/sup r/-1). These sequences have applications in code-division spread-spectrum multiuser communication systems. The families satisfy the Sidelnikov bound with equality on /spl theta//sub max/, which denotes the maximum magnitude of the periodic cross-correlation and out-of-phase autocorrelation values. One of the families satisfies the Welch bound on /spl theta//sub max/ with equality. The linear complexity and the period of all sequences are equal to r(r+3)/2 and 2(2/sup r/-1), respectively, with an exception of the single m-sequence which has linear complexity r and period 2/sup r/-1. Sequence imbalance and correlation distributions are also computed.