In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.n this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.

We study the problem of repairing erasures in locally repairable codes beyond the code locality under the rack-aware model. We devise two repair schemes to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model, by setting each repair set as a rack. The first repair scheme provides optimal repair bandwidth for one rack erasure. We then establish a cut-set bound for locally repairable codes under the rack-aware model. Using this bound we show that our second repair scheme is optimal. Furthermore, we consider the partial-repair problem for locally repairable codes under the rack-aware model, and introduce both repair schemes and bounds for this scenario.

In this paper, we introduce a new concept of list-decoding separable matrices with strength$d$and list size$L$, denoted as$(\overline{d}, L)$-LDSM, for non-adaptive combinatorial group testing, which is a generalized notion of several types of known test matrices such as d-disjunct matrices,$\overline{d}$-separable matrices, and d-union-free codes with fast decoding. We first provide a two-step identifying algorithm for$(\overline{d}, L)$-LDSM of size$n\times m$and show that it can determine all the$\leq d$positives among$m$items in time$O(\max\{nm,\ nL^{d}\})$. Furthermore, we derive a lower bound on the largest rate of$(\overline{d},\ L)$-LDSM for any$L\geq d\geq 2$by random coding with expurgation. In particular, when$L=m 1/d$, the identifying algorithm of$(d,\ m^{1/\overline{d}})$-LDSM is as efficient as that for d-disjunct matrices, while the rate of$(\overline{d},\ m^{1/d})$-LDSM can be significantly larger than that of d-disjunct matrices.

Secure codes with list decoding (SCLDs) were introduced due to their applications in collusion-resistant multimedia fingerprinting for copyright protection. A fundamental research problem is investigating the largest code rates and explicit constructions for SCLDs. So far, the largest code rates of SCLDs with length$n$have been investigated for asymptotically large alphabet size$q$, and explicit constructions of SCLDs are known for only a few specific cases. In this paper, we establish new lower bounds on the largest code rate of SCLDs for a broad range of alphabet size$q$by virtue of the Lovász local lemma, which particularly implies the known results when$q$is asymptotically large. Furthermore, we present a generic algorithmic construction for SCLDs by means of the Moser-Tardos algorithm and demonstrate its linear-time computational complexity.

In this paper we consider combinatorial secure codes in traitor tracing for protecting copyright of multimedia content. First, we introduce a new notion of secure codes with list decoding (SCLDs) for collusion-resistant multimedia fingerprinting, which includes many existing types of fingerprinting codes as special cases. Next, we build efficient identifying algorithms for SCLDs with complete traceability and establish bounds on its largest possible code rate. In comparison with the existing fingerprinting codes, it is shown that SCLDs have not only much more efficient traceability than separable codes but also a much larger code rate than frameproof codes. As a byproduct, new bounds on the largest code rate of binary separable codes are established as well. Furthermore, a two-stage dynamic traitor tracing framework is proposed for multimedia fingerprinting in the dynamic scenario, which could not only efficiently achieve the complete traceability but also provide a much larger capacity than the static scenario.

It has recently been shown that there are no multimedia fingerprinting codes that can find all malicious users when they use arbitrary linear attacks plus adversarial noise. It is shown that such codes exist if the complete recovery property is limited to the IPP property, i.e., the property to find at least one malicious user. Moreover, we extend this property to a property that allows us to detect all users whose contribution to the forgery is large enough. Efficient decoding (tracing traitors) algorithms are developed for these codes.

All-or-nothing transforms (AONT) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have many applications in cryptography and information security. Later the unconditionally secure AONT and their combinatorial characterization were introduced by Stinson. Informally, a combinatorial AONT is an array with the unbiased requirements and its security properties in general depend on the prior probability distribution on the inputs s-tuples. Recently, it was shown by Esfahani and Stinson that a combinatorial AONT has perfect security provided that all the inputs s-tuples are equiprobable, and has weak security provided that all the inputs s-tuples are with non-zero probability. This paper aims to explore on the gap between perfect security and weak security for combinatorial (t, s, v)-AONTs. Concretely, we consider the typical scenario that all the s inputs take values independently (but not necessarily identically) and quantify the amount of information $H(\mathcal{X}\mid \mathcal{Y})$ about any t inputs $\mathcal{X}$ that is not revealed by any s−t outputs $\mathcal{Y}$. In particular, we establish the general lower and upper bounds on $H(\mathcal{X}\mid \mathcal{Y})$ for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases.

Traitor tracing is a mathematical approach of protecting copyright of multimedia content. In this paper we propose a new concept of secure codes with list decoding (SCLD) for collusion-resistant multimedia fingerprinting, which could include many existing classes of fingerprinting codes as special cases. Furthermore, we build an efficient identifying algorithm for SCLD and establish bounds on its largest asymptotic code rate. In comparison with the existing fingerprinting codes, it is shown that SCLD has not only much more efficient traceability than separable codes but also a much larger code rate than frameproof codes.

We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.

All-or-nothing transforms (AONTs) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have numerous applications in cryptography and information security. Later the unconditionally secure AONTs and their combinatorial characterization were introduced by Stinson. Informally, a combinatorial AONT is an array with the unbiased requirements and its security properties in general depend on the prior probability distribution on the inputs$s$-tuples. Recently, it was shown by Esfahani and Stinson that a combinatorial AONT has perfect security provided that all the inputs$s$-tuples are equiprobable, and has weak security provided that all the inputs$s$-tuples are with non-zero probability. This paper aims to explore on the gap between perfect security and weak security for combinatorial$(t,s,v)$-AONTs. Concretely, we consider the typical scenario that all the$s$inputs take values independently (but not necessarily identically) and quantify the amount of information$H(\mathcal {X}|\mathcal {Y})$about any$t$inputs$\mathcal {X}$that is not revealed by any$s-t$outputs$\mathcal {Y}$. In particular, we establish the general lower and upper bounds on$H(\mathcal {X}|\mathcal {Y})$for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases. Furthermore, the discussions are extended for the security properties of combinatorial asymmetric AONTs.

The Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes is studied. An improved bound is presented by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

BCH codes are among the best practical cyclic codes widely used in consumer electronics, communication systems, and storage devices. However, not much is known about BCH codes with large minimum distance. In this paper, we consider narrow-sense BCH codes of length $n = \frac{q^m-1}{N}$ with designed distance $\delta = \frac{s}{q-1}n$ proportional to $n$, where $N$ divides $\frac{q^m-1}{q-1}$ and $1 \le s \le q-1$. We determine both their dimensions and minimum distances. In particular, when $N=1$, the codes are primitive, with minimum distance $d=\frac{s}{q-1}(q^m-1)$ and dimension $k = (q-s)^m$. The general result on code dimensions is achieved by applying generating functions and inverse discrete Fourier transforms to an enumeration problem.

In this paper, we study binary signature codes for the weighted binary adder channel (WbAC) and collusion-resistant multimedia fingerprinting. Let A(n, t) denote the maximum size of a t-signature code of length n, and A(n, w, t) denote the maximum size of a t-signature code of length n and constant-weight w. First, we derive asymptotic and general upper bounds on A(n, t) by relating signature codes to Bt codes and bipartite graphs with large girth respectively, and also show the upper bounds are tight for certain cases. Second, we determine the exact values of A(n, 2, 2) and A(n, 3, 2) for infinitely many n by connecting signature codes with C4-free graphs and union-free families, respectively. Third, we provide two explicit constructions for t-signature codes which have efficient decoding algorithms and applications to two-level signature codes. Furthermore, we show from a geometric viewpoint that there does not exist any binary code with complete traceability for noisy WbAC and multimedia fingerprinting. A new type of signature codes with a weaker requirement than complete traceability is introduced for the noisy scenario.

This paper investigates reducing sub-packetization of capacity-achieving schemes for uncoded Storage Constrained Private Information Retrieval (SC-PIR) systems. In the SC-PIR system, a user aims to download one out of K files from N servers while revealing nothing about the identity of the requested file to any individual server, in which the K files are stored at the N servers in an uncoded form and each server can store up to μK equivalent files, where μ is the normalized storage capacity of each server. We first prove that there exists a capacity-achieving SC-PIR scheme for a given storage design if and only if all the packets are stored exactly at M\triangleq μN servers for μ such that M=μN ∈ {2,3,...,N}. Then, the optimal sub-packetization for capacity-achieving linear SC-PIR schemes is characterized as the solution to an optimization problem, which is typically hard to solve since it involves non-continuous indicator functions. Moreover, a new notion of array called Storage Design Array (SDA) is introduced for the SC-PIR system. With any given SDA, an associated capacity-achieving SC-PIR scheme is constructed. Next, the SC-PIR schemes that have equal-size packets are investigated. Furthermore, the optimal equal-size sub-packetization among all capacity-achieving linear SC-PIR schemes characterized by Woolsey et al. is proved to be \frac N(M-1)gcd(N,M), which is achieved by a construction of SDA. Finally, by allowing unequal size of packets, a greedy SDA construction is proposed, where the sub-packetization of the associated SC-PIR scheme is upper bounded by \frac N(M-1)gcd(N,M). Among all capacity-achieving linear SC-PIR schemes, the sub-packetization is optimal when min{M,N-M}|N or M=N, and within a multiplicative gap \frac min{M,N-M}gcd(N,M) of the optimal one in general. In particular, for the special case N=d·M±1 where the positive integer d ≥ 2, we propose another SDA construction to obtain lower sub-packetization.

In this paper, locally repairable codes which have optimal minimum Hamming distance with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds apply to more general cases, and have weaker requirements compared with the known ones. In this sense, they both improve and generalize previously known bounds. Further, optimal codes are constructed, whose length is order-optimal with respect to the new upper bounds. Notably, the length of the codes is super-linear in the alphabet size.

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, a new combination of codes with locality and codes with multiple disjoint repair sets (also called availability) is introduced. Accordingly, a Singleton-type bound is derived for the new code, which contains those bounds in [9], [20], [28] as special cases. Optimal constructions are proposed with respect to the new bound. In addition, these constructions can also generate optimal codes with multiple disjoint repair sets with respect to the bound in [28], which to the best of our knowledge, are the first explicit constructions that can achieve the bound in [28].

Optimal locally repairable codes with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known bounds. Optimal codes are constructed, whose length is order optimal when compared with the new upper bounds. The length of the codes is super linear in the alphabet size.

Parent-identifying schemes provide a way to identify causes from effects for some information systems, such as digital fingerprinting and group testing. In this paper, we consider the combinatorial structures for parent-identifying schemes. First, we establish an equivalent relationship between the parent-identifying schemes and forbidden configurations. Based on this relationship, we derive the probabilistic existence lower bounds for two related combinatorial structures, that is, t-parent-identifying set systems (t-IPPS) and t-multimedia parent-identifying codes (t-MIPPC), which are used in broadcast encryption and multimedia fingerprinting, respectively. The probabilistic lower bound for the maximum size of a t-IPPS has the asymptotically optimal order of magnitude in many cases, and that for t-MIPPC provides the asymptotically optimal code rate when t = 2 and the best known asymptotic code rate when t ≥ 3. Furthermore, we analyze the structure of 2-IPPS and prove some bounds for certain cases.

The Stinson-Wei traceability scheme (known as traceability scheme) was proposed for broadcast encryption as a generalization of the Chor-Fiat-Naor traceability scheme (known as traceability code). Cover-free family was introduced by Kautz and Singleton in the context of binary superimposed code. In this paper, we find a new relationship between a traceability scheme and a cover-free family, which strengthens the anti-collusion strength from t to t2, i.e., a t-traceability scheme is a t2-cover-free family. Based on this interesting discovery, we derive new upper bounds for traceability schemes. By using combinatorial structures, we construct several infinite families of optimal traceability schemes, which attain our new upper bounds. We also provide a constructive lower bound for traceability schemes, the size of which has the same order of magnitude as our general upper bound. Meanwhile, we consider parent-identifying set systems, an anti-collusion key-distributing scheme requiring weaker conditions than traceability scheme but stronger conditions than cover-free family. A new upper bound is also given for parent-identifying set systems.

As an optimal combinatorial object, zero-difference balanced (ZDB) functions introduced by Ding in 2008, are a generalization of the well-known perfect nonlinear functions. ZDB functions have received much attention in recent years due to its important applications in coding theory and sequence design. One objective of this paper is to present a construction of ZDB functions based on a kind of generalized cyclotomy. It generates ZDB functions over cyclic group with new parameters which can not be produced by earlier constructions. Another objective of this paper is to employ these ZDB functions to obtain at the same time: 1) optimal constant-composition codes; 2) perfect difference systems of sets; and 3) optimal frequency-hopping sequences, all with new parameters.

Frameproof codes are used to fingerprint digital data. They can prevent copyrighted materials from unauthorized use. In this paper, we study upper and lower bounds for$w$-frameproof codes of length$N$over an alphabet of size$q$. The upper bound is based on a combinatorial approach and the lower bound is based on a probabilistic construction. Both bounds can improve one of the previous results when$q$is small compared with$w$, say$cq\leq w$for some constant$c\leq q$. Furthermore, we pay special attention to binary frameproof codes. We show a binary$w$-frameproof code of length$N$cannot have more than$N$codewords if$N<\binom {w+1}{2}$.

Let $$\mathbb{C }$$ be a code of length $$n$$ over an alphabet of $$q$$ letters. The descendant code $$\mathsf{desc}(\mathbb C _0)$$ of $$\mathbb C _0 = \{\mathbf{c}^1, \mathbf{c}^2, \ldots , \mathbf{c}^t\} \subseteq \mathbb{C }$$ is defined to be the set of words $$\mathbf{x} = (x_1, x_2, \ldots ,x_n)$$ such that $$x_i \in \{c^1_i, c^2_i, \ldots , c^t_i\}$$ for all $$i=1, \ldots , n$$ . $$\mathbb{C }$$ is a $$\overline{t}$$ -separable code if for any two distinct $$\mathbb{C }_1, \mathbb{C }_2 \subseteq \mathbb{C }$$ such that $$|\mathbb{C }_1| \le t$$ , $$|\mathbb{C }_2| \le t$$ , we always have $$\mathsf{desc}(\mathbb{C }_1) \ne \mathsf{desc}(\mathbb{C }_2)$$ . The study of separable codes is motivated by questions about multimedia fingerprinting for protecting copyrighted multimedia data. Let $$M(\overline{t},n,q)$$ be the maximal possible size of such a separable code. In this paper, we provide an improved upper bound for $$M(\overline{2},2,q)$$ by a graph theoretical approach, and a new lower bound for $$M(\overline{2},2,q)$$ by deleting suitable points and lines from a projective plane, which coincides with the improved upper bound in some places. This corresponds to the bounds of maximum size of bipartite graphs with girth $$6$$ and a construction of such maximal bipartite graphs.

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. Separable codes can be used to construct fingerprints resistant to the averaging collusion attack on multimedia contents. In this paper, we investigate -separable codes from a combinatorial point of view. We first derive several upper bounds on the sizes of -separable codes, and then turn our attention to the constructions of optimal -separable codes with short length. Two infinite families of optimal -separable codes of length 2 are constructed from projective planes, and all optimal -separable codes of length 3 are explicitly constructed by means of difference matrices. These optimal -separable codes with short length can be used to construct good -separable codes with long length by a known composition construction.

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. AND anti-collusion codes can be used to construct fingerprints resistant to collusion attacks on multimedia contents. In this paper, we first investigate AND anti-collusion codes and related detection algorithms from a combinatorial viewpoint, and then introduce a new concept of logical anti-collusion code to improve the traceability of multimedia fingerprinting. It reveals that frameproof codes have traceability for multimedia contents. Relationships among anti-collusion codes and other structures related to fingerprinting are discussed, and constructions for both AND anti-collusion codes and logical anti-collusion codes are provided.

The notion of a monotonic directed design was introduced to construct difference triangle sets by Chu, Colbourn, and Golomb [SIAM J. Discrete Math., 18 (2005), pp. 741–748]. In this paper, we describe various constructions for monotonic directed designs and establish the necessary and sufficient conditions for the existence of a monotonic directed design with block size 3, and with block size 4 leaving two definite exceptions and six possible exceptions.

Motivated by applications in combinatorial group testing for consecutive positives, we investigate a block sequence of a maximum packing $MP (t,k,v)$ which contains the blocks exactly once such that the collection of all blocks together with all unions of two consecutive blocks of this sequence forms an error correcting code with minimum distance d. Such a sequence is usually called a block sequence with consecutive unions having minimum distance d, and denoted by $BSCU (t,k,v|d)$. In this paper, we show that the necessary conditions for the existence of $BSCU (3,4,v|4)$s of Steiner quadruple systems, namely, $v\equiv2,4$ (mod 6) and $v\geq4$, are also sufficient, excepting $v=8,10$.

Frequency hopping (FH) sequences play a key role in frequency hopping spread spectrum communication systems. In order to evaluate the performance of FH sequences, Lempel and Greenberger (1974) and Peng and Fan (2004) derived lower bounds on their Hamming auto- and cross-correlations. In this paper, we construct families of FH sequences with Hamming correlations meeting those bounds by combinatorial and algebraic techniques. We first construct optimal families consisting of a single FH sequence with maximum Hamming correlation equal to 2 from a combinatorial approach. Then we investigate families consisting of multiple FH sequences. We provide a combinatorial characterization for such families, and present a recursive method to construct them by means of this characterization. We also describe two algebraic constructions for such families of FH sequences, generalizing those of Ding, Moisio, and Yuan (2007). As a consequence, many new optimal families of FH sequences are obtained.

The radar array problem arises from the need to design frequency hopping sequences with small out-of-phase autocorrelations. It assumes the reflected signals have negligible Doppler shifts, so the correlations are calculated along the time axis only. In this correspondence, a systematic construction for radar arrays is provided by means of homogeneous uniform difference matrices. A systematic construction for properly centered permutation matrices, a special kind of homogeneous uniform difference matrices, is also provided, which partially solves the open problems posed by Zhang and Tu.

The notion of a splitting authentication code is very important in the context of an authentication code with arbitration. Ogata et al. [Discrete Math., 279 (2004), pp. 383--405] characterized an optimal splitting authentication code in terms of a splitting balanced incomplete block design (BIBD). A $(v,u \times c,1)$-splitting BIBD is a pair $({\cal V}, {\cal B})$, where ${\cal V}$ is a v-set of points and ${\cal B}$ is a collection of $u \times c$ arrays, called blocks, with entries from ${\cal V}$, such that any point of ${\cal V}$ can occur at most once in any block, and forany two distinct points x and y of ${\cal V}$, there is exactly one block of ${\cal B}$ in which x and y occur in different rows. In this paper, we describe various combinatorial constructions for splitting BIBDs (or, equivalently, optimal splitting authentication codes). We show that the necessary conditions for the existence of a $(v,u \times c,1)$-splitting BIBD (or, equivalently, an optimal c-splitting authentication code with u source states and v messages) are also sufficient for (u,c) = (2,2t) for any positive integer t,(u,c) = (2,3) with a definite exception of v = 10,(u,c) = (3,2) with a definite exception of v =9, and (u,c) = (4,2) with two possible exceptions of v = 49,385.

Frequency hopping multiple access (FHMA) spread-spectrum communication systems employing multiple frequency-shift keying (MFSK) as data modulation technique are investigated from a combinatorial approach. A correspondence between optimal frequency hopping (FH) sequences and partition-type difference packings is first established. By virtue of this correspondence, FHMA systems with a single optimal FH sequence each are constructed from various combinatorial structures such as affine geometries, cyclic designs, and difference families. Combinatorial recursive constructions are also presented. Many new infinite series of optimal FH sequences are thus obtained. These new FH sequences are also useful in ultra wideband (UWB) communication systems.

A (v,k,/spl lambda/) optical orthogonal code C is a family of (0,1) sequences of length v and weight k satisfying the following correlation properties: 1) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/x/sub t+i//spl les//spl lambda/ for any x=(x/sub 0/, x/sub 1/, ..., x/sub v-1/)/spl isin/C and any integer i/spl ne/0(mod v); 2) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/y/sub t+i//spl les//spl lambda/ for any x=(x/sub 0/, x/sub 1/, ..., x/sub v-1/)/spl isin/C, y=(y/sub 0/, y/sub 1/, ..., y/sub v-1/)/spl isin/C with x/spl ne/y, and any integer i, where the subscripts are taken modulo v. A (v,k,/spl lambda/) optical orthogonal code (OOC) with /spl lfloor/(1/k)/spl lfloor/(v-1/k-2)/spl lfloor/(v-2/k-2)/spl lfloor//spl middot//spl middot//spl middot//spl lfloor/(v-/spl lambda//k-/spl lambda/)/spl rfloor/$: M/spl rfloor//spl rfloor//spl rfloor/ codewords is said to be optimal. OOCs are essential for success of fiber-optic code-division multiple-access (CDMA) communication systems. The use of an optimal OOC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, various combinatorial constructions for optimal (v,4,1) OOCs, such as those via skew starters and Weil's theorem on character sums, are given for v/spl equiv/0 (mod 12). These improve the known existence results on optimal OOCs. In particular, it is shown that an optimal (v,4,1) OOC exists for any positive integer v/spl equiv/0 (mod 24).

Optimal (9p,4,1) optical orthogonal codes (OOCs) are constructed for all primes p congruent to 1 modulo 4. Direct constructions with explicit codewords are presented for the case $p \equiv 13 \ \mbox{mod} \ 24$, and Weil's theorem on character sums is used to settle the cases $p \equiv 1,5,17 \ \mbox{mod} \ 24$. By applying a known recursive construction, optimal (9v,4,1)-OOCs are obtained for all v, a product of primes congruent to 1 modulo 4.

A (v, k, /spl lambda//sub a/, /spl lambda//sub c/) optical orthogonal code (OOC) C is a family of (0, 1)-sequences of length v and weight k satisfying the following two correlation properties: (1) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/x/sub t+i//spl les//spl lambda//sub a/ for any x=(x/sub 0/,x/sub 1/,/spl middot//spl middot//spl middot/,x/sub v-1/)/spl isin/C and any integer i not equivalent 0 mod v; and (2) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/y/sub t+i//spl les//spl lambda//sub b/ for any x=(x/sub 0/,x/sub 1/,/spl middot//spl middot//spl middot/, x/sub v-1/) /spl isin/ C, y=(y/sub 0/,y/sub 1/,/spl middot//spl middot//spl middot/,y/sub v-1/) /spl isin/C with x/spl ne/y, and any integer i, where the subscripts are taken modulo v. The study of optical orthogonal codes is motivated by an application in optical code-division multiple-access communication systems. In this paper, upper bounds on the size of an optical orthogonal code are discussed. Several new constructions for optimal optical orthogonal codes with weight k/spl ges/4 and correlation constraints /spl lambda//sub a/=/spl lambda//sub c/=1 are described by means of optimal cyclic packings. Many new infinite series of such optimal optical orthogonal codes are thus produced.