On generator polynomial matrices of generalized pseudo-cyclic codes

In this paper, generalized pseudo-cyclic (GPC) codes are proposed and their basic properties are investigated. Generator polynomial matrices of GPC codes are constructively defined and thereby a dimension formula for GPC codes is provided. While a pseudo-cyclic code is equal to an ideal of the ring which consists of polynomials modulo a fixed polynomial, a GPC code is equal to a submodule of the direct sum of the rings which consist of polynomials modulo fixed polynomials. In the theory of cyclic codes and PC codes, Euclidean division algorithm for polynomials is essential; its generalization for polynomial vectors is obtained and enables us with generator polynomial matrices to encode GPC codes fast and systematically.