Generating Idempotents of Sixth Residue Codes over the Binary Field

Abstract

Higher power residue codes over finite fields are generated by factors of the polynomial 1 n x − . Unfortunately, to decompose the polynomial 1 n x − over finite fields is difficult. Generating idempotents can also generate higher power residue codes. Thus it is important to get generating idempotents of cyclic codes. We find precise expressions of generating idempotents of some sixth residue codes of length over the binary field, where p is a prime such that p º1(mod 24) .