On Majority-Logic Decoding for the Duals of Primitive Polynomial Codes

摘要

The class of polynomial codes introduced by Kasami et al. has considerable inherent algebraic and geometric structure. It has been shown that this class of codes and their dual codes contain many important classes of cyclic codes as subclasses, such as BCH codes, Reed-Solomon codes, generalized Reed-Muller codes, projective geometry codes and Euclidean geometry codes. The purpose of this paper is to investigate further properties of polynomial codes and their duals. First, majority-logic decoding for the duals of certain primitive polynomial codes are considered. Two methods of forming orthogonal parity-check sums are presented. Second, the maximality of Euclidean geometry codes is proved. The necessary and sufficient condition for the roots of the generator polynomial of an Euclidean geometry code is derived. (Author)