Minimal cyclic codes of length 16p^n over GF(q), where q is prime or prime power of the form 16k+7

Abstract

In this paper, the expressions for primitive idempotents in group algebra of cyclic group G of length $16p^n$, where $p$ is prime and $q$ is some prime or prime power (of type $16k+7$), $n$ is a positive integer, order of $q$ modulo $p^n$ is $\frac{\phi(p^n)}{2}$, are obtained. Associated with this the generating polynomials and minimum distance bounds for the corresponding cyclic codes are obtained.