Irreducible cyclic codes of length 16pn and their parameters

Abstract

This paper derives the expressions for primitive idempotents for semi simple ring Rn​=(xn−1)GF(q)[x]​, where, p and q (of type 16k + 1) are distinct odd primes, n is an integer that is positive and od(q) modulo pn is . Among other results, we derive the minimum distance bounds and the generating polynomials for the related irreducible cyclic codes.