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...

In this paper, we evaluate the performance of BCH (Bose-ChaudhuriHocquenghem) correcting codes when used to protect data over a land mobile channel using OFDM (Orthogonal Frequency Division Multiplexing) modulation. To deal with memory channels, the Gilbert-Elliott (GE) model was considered to simulate a Rayleigh fading channel and BCH codes to analyse the error process. Relating GE parameters ...

It has been suggested that system L (LAT1/CD98hc) is up-regulated in cancer cells, including breast tumour cells, and is therefore a promising molecular target to inhibit or limit tumour cell growth. In view of this, we have examined the effect of BCH and other inhibitors of system L on the growth of MCF-7, ZR-75-1 and MDA-MB-231 cells. Treating cells with BCH markedly inhibited the metabolism ...

Error correction is one of the important technique for detecting and correcting errors in communication channels, memories etc. , Errors are associated with all types of memories. But the NAND FLASH memories are competing in the market due to its low power, high density, cost effectiveness and design scalability. As far as the memory is concerned the testing should not consume more time. So, so...

By using the theory ofjinite5eld Fourier transforms, the subject of rror control codes is described in N language familiar to thejield of signal processing. The many importunt uses of spectral techniques in error control are summarized. Many classes of linear codes are given a spectral interpretation and some new codes are described, Several nlternative encoder1 decoder schemes are described by...

Some generalizations of BCI algebras (the RM, BH, CI, BCH,
 BH**, BCH**, and *aRM** algebras) satisfying the identity $(x \rightarrow
 1)\rightarrow y = (y \rightarrow 1) x$ are considered. The connections these algebras
 various commutative groups (such as, for
 example, involutive moons (weakly)
 goops) described. In particular, it is proved that an RM
 algebra v...

Mobile nodes can encounter many challenges in underwater environments during communication due to turbidity, suspended particles, small bubbles, and turbulence. These factors cause absorption scattering, ultimately corrupting optical signals. Error-correcting codes be used correct certain corrupted bits thus reduce the errors a channel. In this work, Bose-Chaudhuri-Hocquenghem (BCH) (31, 16)-co...