The watermark signals are weakly inserted in images due to imperceptibility constraints which makes them prone to errors in the extraction stage. Although the error correcting codes can potentially improve their performance one must pay attention to the fact that the watermarking channel is in general very noisy. We have considered the trade-o of the BCH codes and repetition codes in various co...

This paper considers Bose-Chaudhuri-Hocquenghem (BCH) codes for distributed source coding. A feedback channel is employed to adapt the rate of the code during the decoding process. The focus is on codes with short block lengths for independently coding a binary source X and decoding it given its correlated side information Y. The proposed codes have been analyzed in a high-correlation scenario,...

Absfruct-Goppa described a new class of linear noncyclic errorcorrecting codes in [l] and [2]. This paper is a summary of Goppa’s work, which is not yet available in English.’ We prove the four most important properties of Goppa codes. 1) There exist q-ary Goppa codes with lengths and redundancies comparable to BCH codes. For the same redundancy, the Goppa code is typically one digit longer. 2)...

A four-year project to build capacity in developing and transition countries to participate effectively in the Biosafety Clearing-House (BCH) has resulted in a well-trained and effective team of BCH Regional Advisors, an extensive and continually improving body of training materials, and a growing number of participating countries. Throughout the project, the training and the materials have inc...

Motivated by the problem of nding light (i.e., low weight) and short (i.e., low degree) codewords in narrow-sense, primitive BCH codes we consider the problem of determining the probability that a random t-set of vectors in an n dimensional vector space over GF (q) contains an r-dimensional subspace (or aane subspace). We nd some bounds for this and similar probabilities and apply these techniq...

| BCH decoding usually involves the evaluation of the error-locator polynomial. This is often achieved with the Berlekamp-Massey algorithm. The evaluation of the error-locator polynomial may also be computed using fast inversion techniques for Hankel matrices. It can be shown that O(lt) steps are necessary, with l being the number of errors which occurred and t being the error-correction capabi...

We consider primitive cyclic codes of length p − 1 over Fp. The codes of interest here are duals of BCH codes. For these codes, a lower bound on their minimum distance can be found via the adaptation of the Weil bound to cyclic codes (see [10]). However, this bound is of no significance for roughly half of these codes. We shall fill this gap by giving, in the first part of the paper, a lower bo...

In this paper, a Bose-Chaudhuri-Hocquenghem (BCH) coder in the field of the real numbers is investigated for simultaneous source coding and impulse noise cancellation of satellite images. Our channel is a binary symmetric channel (BSC). Our approach is to make a carefully designed interpolation of the subband images prior to quantization and transmission. Compared to a classical tandem source a...

The Baker-Campbell-Hausdorff (BCH) series and the Zassenhaus product are of fundamental importance for the theory of Lie groups and their applications in physics. In this paper, various methods for the computation of the terms in these expansions are compared, and a new efficient approach for the calculation of the Zassenhaus terms is introduced. Mathematica implementations for the most efficie...

In this paper we study the family of cyclic codes such that its minimum distance reaches the maximum of its BCH bounds. We also show a way to construct cyclic codes with that property by means of computations of some divisors of a polynomial of the form xn − 1. We apply our results to the study of those BCH codes C, with designed distance δ, that have minimum distance d(C) = δ. Finally, we pres...