Dimension of nonbinary antiprimitive BCH codes

12/19/2017

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by   Ruihu Li, et al.

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Bose-Chaudhuri-Hocquenghem (BCH) codes have been widely employed in satellite communications, compact disc players, DVDs, disk drives, solid-state drives, two-dimensional bar codes and in cryptography more recently. However, there is only a little known about primitive BCH codes, let alone nonprimitive ones. In this paper, dimension of a special class of nonprimitive BCH codes of length n=q^m+1 ( which are also called antiprimitive BCH codes) are studied. Some new approaches, such as iterative algorithm, partition and scaling, are adopted to determine the first several largest coset leaders modulo n=q^2t+1+1 along with coset leaders of C_x modulo n=q^m+1 for q^m/2<x<2(q^m/2+q). After deriving the cardinalities of these cyclotomic cosets, we shall calculate precisely dimension of some antiprimitive BCH codes.