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...

Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes – a family of cyclic codes – in practice. In theory, BCH codes are among the best cyclic codes in terms of their error-correcting capability. A subclass of BCH codes are the narrow-sense primitive BCH codes. However, ...

We define the notion of radical in BCH-algebra and investigate the structure of [X; k], a viewpoint of radical in BCH-algebras. 1. Introduction. In 1966, Imai and Iséki [8] and Iséki [9] introduced two classes of abstract algebras: BCK-algebras and BCI-algebras. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. In 1983, Hu and Li [5, 6] introduced a w...

Modular reduction is the basic building block of many publickey cryptosystems. BCH codes require repeated polynomial reductions modulo the same constant polynomial. This is conceptually very similar to the implementation of public-key cryptography where repeated modular reduction in Zn or Zp are required for some fixed n or p. It is hence natural to try and transfer the modular reduction expert...

VLSI Architectures for Modern Error-Correcting Codes CRC Press Book. Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes, and binary. An important class of multipleerror-correcting linear cyclic codes is the class of BCH codes. In fact, BCH code is a generalization of the cyclic Hamming codes. Error correction codes (ECCs) are deployed in digital communication systems to tion 4 recalls...

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