In this paper we investigate the structure of quasi-BCH codes. In the first part of this paper we show that quasi-BCH codes can be derived from Reed-Solomon codes over square matrices extending the known relation about classical BCH and Reed-Solomon codes. This allows us to adapt the Welch-Berlekamp algorithm to quasi-BCH codes. In the second part of this paper we show that quasi-BCH codes can ...

Let q = 3l+2 be a prime power. Maximal designed distances of imprimitive Hermitian dual containing q2-ary narrow-sense (NS) BCH codes of length n = (q 6−1) 3 and n = 3(q 2 −1)(q2 +q+1) are determined. For each given n, non-narrow-sense (NNS) BCH codes which achieve such maximal designed distances are presented, and a series of NS and NNS BCH codes are constructed and their parameters are comput...

The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real an...

BCH codes have been studied for over fifty years and widely employed in consumer devices, communication systems, and data storage systems. However, the dimension of BCH codes is settled only for a very small number of cases. In this paper, we study the dimensions of BCH codes over finite fields with three types of lengths n, namely n = qm − 1, n = (qm − 1)/(q− 1) and n = qm +1. For narrow-sense...

Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper. The first one is derived from q-ary Steane’s enlargement of CSS codes applied to nonnarrow-sense BCH codes. The second one is derived from the method of defining sets of classical cyclic codes. The asymmetric quantum BCH codes and subs...

Cyclic codes over finite fields are widely employed in communication systems, storage devices and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. A subclass of good BCH codes are the narrow-sense BCH codes over GF(q) with length n = (qm−1)/(q−1). Little is known about ...

The purpose of this study was to examine the effect of 2-aminobicyclo-(2,2,1)-heptane-2-carboxylic acid (BCH), an inhibitor of L-type amino acid transporters, on the cell growth suppression in KB human oral cancer cells and to study the roles of cell cycle regulatory factors in the BCH-induced growth inhibition. The effect of BCH on cell growth suppression and the influence of BCH to cell cycle...