Dimension of nonbinary antiprimitive BCH codes

Bose-Chaudhuri-Hocquenghem (BCH) codes have been widely employed in satellite communications, compact disc players, DVDs, disk drives, solidstate 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 + 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+1 along with coset leaders of Cx modulo n = q +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.