In this study, random codes are applied to the classical syndrome coding scheme to achieve secrecy of communications. By analysing the effect of the values of the columns of the parity check matrix on the resulting security level of communications, a code design method is presented which constructs a class of random codes, termed random permutation codes, which achieve high security levels and are easily generated. A theoretical analysis method is presented which determines the security level achieved by randomly chosen, linear binary codes, and compared with simulation results obtained by Monte Carlo analysis. The results verify the theoretical approach. In particular, the theoretical method is also suitable for analysis of long codes having a large number of parity check bits which are beyond evaluation by computer simulation. The results show that the security performance of any randomly chosen permutation code is close to that of the best equivocation code having the same code parameters. This has the practical advantage in syndrome coding of being able to use an ephemeral code for each communication session, thereby providing forward secrecy, a desired feature of modern, secure communication systems.

It is shown that for some location sets and some integral multiple power Galois fields that some new general subclasses of Goppa codes may be defined which have improved lower bounds to code dimension and minimum distance compared with ordinary Goppa codes. Some previously published results are shown to be particular cases of these general subclasses of codes. A new subclass of reversible Goppa codes is also presented. Examples of code construction for these subclasses, demonstrating the improved code parameters, are presented for both non binary and binary codes.

In this paper, we propose a chain based syndrome coding scheme for secure communication in a wiretap channel, where the main channel is noiseless and the eavesdropper channel is binary symmetric. The most relevant aspect of the scheme, which represents a generalization of Wyner's conventional syndrome coding scheme, relates to the use of a chain of syndromes to encode the message. By using the eavesdropper decoder output equivocation to measure the security of the scheme, extensive analytic and numerical results demonstrate that the chain based syndrome coding scheme exhibits significantly lower information leakage than the conventional syndrome coding scheme.

Traditionally, codes are designed for an error correcting system to combat noisy transmission channels and achieve reliable communication. These codes can be used in syndrome coding, but it is shown in this study that the best performance is achieved with codes specifically designed for syndrome coding. In the view of the security of the communication, the best codes are the codes, which have the highest value of an information secrecy metric, the equivocation rate, for a given code length and code rate and are well packed codes. A code design technique is described, which produces the best binary linear codes for the syndrome coding scheme. An efficient recursive method to determine the equivocation rate for the binary symmetric channel and any linear binary code is also presented. A large online database of best equivocation codes for the syndrome coding scheme has been produced using the code design technique with some examples presented in the study. The presented results show that the best equivocation codes produce a higher level of secrecy for the syndrome coding scheme than almost all best known error correcting codes. Interestingly, it is unveiled that some outstanding best known error correcting codes are also best equivocation codes.

We present a generalized construction of extended length Goppa codes. Using this construction, we obtain 71 new codes in finite field Fqfor q = 4, 7, 8, 9 with better minimum distance than the previously known codes with the same length and dimension.

Goppa codes have some of the largest minimum distances possible for linear codes. The authors use some binary Goppa codes in which four new binary codes are obtained with parameters better than any codes known to date. The authors also present the necessary conditions for a code obtained by shortening a longer code which will have a greater minimum distance than the original code.

We present an efficient construction of extended length Goppa codes. Using this construction, we obtain 78 new nonbinary codes with better minimum distance than the previously known codes with the same length and dimension. The construction is based on the observation that certain Goppa codes can be seen as BCH codes.

We consider communication between a legitimate transmitter and a legitimate receiver in the presence of an eavesdropper in the conventional Gaussian wiretap channel setting. Based on Wyner's coding scheme, we show that a code construction using orthogonal codewords can achieve the secrecy capacity of the Gaussian wiretap channel in the wideband regime. This is illustrated through analysis of the error probability between the legitimate parties and the eavesdropper equivocation rate, as well as various simulation results.

Algebraic geometry codes or Goppa codes are defined with places of degree one. In constructing generalised algebraic geometry codes places of higher degree are used. In this paper we present 41 new codes over F16which improve on the best known codes of the same length and rate. The construction method uses places of small degree with a technique originally published over 10 years ago for the construction of generalised algebraic geometry codes.

This paper investigates the application of high capacity watermarking in still images. The performance of two orthogonalisation schemes and one writing-on-dirty-paper scheme are discussed. Orthogonalisation is an embedding technique which uses sequences that are orthogonal to the cover image modulating the payload information. Writing-on-dirty- paper uses the codewords which have the maximum cross- correlation of the cover image to carry the message. Aspects of comparison are: 1) watermark fidelity, 2) payload capacity and 3) robustness. The watermark fidelity is measured using Watson's perceptual model and mean squared error. Given fixed fidelity levels the payload capacity is measured in terms of bit error rate. Additive White Gaussian Noise (AWGN) with different variances is used to evaluate the robustness of the watermarks. Results are presented which categories the advantages and disadvantages of each scheme, under different situations. Certain trade-offs must be considered for specific requirement.

A new method of finding binary cyclic codes from the finite-field transform domain is presented. These cyclic codes have sparse parity-check matrix and thus are suitable for iterative decoding. Some interesting properties of the proposed construction method include the knowledge of the minimum distance and the ability to trade the increase in code dimension with a reduction in the parity-check matrix sparsity. By means of simulations, we show that the error correcting performance of the codes under iterative decoding is very close to the sphere-packing-bound constrained for binary transmission.

A method is presented where a parallel concatenated convolutional code is preceded with a short cyclic redundancy check (CRC) without code rate loss. Parity bits are punctured and their place taken by the CRC. Results are given for the weight spectrum of an optimised code, rate 2/3, codeword length, n=1014 in comparison with an optimised, nonCRC code using the same rate and codeword length. Frame error rate performance achieved is within 0.36dB of the sphere packing bound constrained for binary transmission.