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Erschienen in:
2018 | OriginalPaper | Buchkapitel
A Method to Enlarge the Design Distance of BCH Codes and Some Classes of Infinite Optimal Cyclic Codes
verfasst von : Shanding Xu, Xiwang Cao, Chunming Tang
Erschienen in: Information Security and Cryptology
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Abstract
Cyclic codes are a meaningful class of linearcodes due to their effective encoding and decoding algorithms. As a subclass of cyclic codes, Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes have good error-correcting capability and are widely used in communication systems. As far as the design of cyclic codes is concerned, it is difficult to determine the minimum distance. It is well known that the minimum distance of a cyclic code of designed distance d is at least d. In this paper, by adjusting the generator polynomial slightly and using a concatenation technique, we present a method to enlarge the designed distance of cyclic codes and obtain two classes of \([pq,q-1,2p]\) cyclic codes and \([pq,p-1,2q]\) cyclic codes over GF(2). As a consequence, a class of infinite optimal [3p, 2, 2p] cyclic codes, where \(p\equiv {-1}\pmod 8\), with respect to the Plotkin bound over GF(2) is presented.