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This paper presents a more efficient algorithm to count codewords of given weights in self-dual double-circulant and formally self-dual quadratic double-circulant codes over GF(2). A method of deducing the modular congruence of the weight distributions of the binary quadratic double-circulant codes is proposed. This method is based on that proposed by… (More)
An efficient algorithm to count all codewords of given weight and a method to deduce the modular congruence of the weight distributions of the binary quadratic double-circulant codes are presented. Using this algorithm, we give the weight distribution of the quadratic double-circulant code of length 168 and that of the extended quadratic-residue code of the… (More)
We show how to construct an algorithm to search for binary idempotents which may be used to construct binary LDPC codes. The algorithm, which allows control of the key properties of sparseness, code rate and minimum distance, is constructed in the Mattson-Solomon domain. Some of the new codes, found by using this technique, are displayed.
— Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2 m), where m > 0 cyclic low-density parity-check codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this… (More)
The Hamming weight enumerator function of the formally self-dual even, binary extended quadratic residue code of prime p = 8m + 1 is given by Gleason's theorem for singly-even code. Using this theorem, the Hamming weight distribution of the extended quadratic residue is completely determined once the number of codewords of Hamming weight j Aj, for 0 ≤ j ≤… (More)
In this paper we propose a new high capacity, low energy requirement, and robust spread spectrum watermark approach for still images. This approach uses an orthogonalisation scheme to generate a set of binary spread spectrum carriers that are able to minimize the interference of the original image on the watermark information detection, so that, more than… (More)
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.
— This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a Multi-Guess Algorithm extended from the Guess Algorithm and a new algorithm – the In-place Algorithm. The Multi-Guess… (More)
A special case of wiretap channel is studied and analysed when the main channel is an error free channel and the eavesdropper channel is a binary symmetric channel. The goal of this work is to maximise the equivocation on the eavesdropper side by using a combination of the technique of the McEliece cryptosystem using Best Known Linear Codes(BKLC) coupled… (More)