Cycle representatives of quasi-irreducible two-dimensional cyclic codes

摘要

The author presents a method of finding the cycle representatives of any quasi-irreducible (QIR) 2-D cyclic code by extending A.P. Kurdjukov's (Probl. Peredach. Inform., vol.12, no.4, p.107-8, 1976) result on quasi-irreducible (i.e. nonsquare-free) 10D cyclic codes. The algorithm is not strictly deterministic in the sense that it is necessary to obtain a set of representative arrays for the code by a trial-and-error method. The result is useful for finding the cycle representatives of any 2D cyclic code by combining QIR components with the aid of G. Sequin's (1974) method to the case where the symbol field is the binary Galois field GF(2). In particular, the result is useful for determining the weight distribution of any two-dimensional cyclic code.