Cycle representatives of quasi-irreducible two-dimensional cyclic codes

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