### 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.

**Published:**2019-10-10

**How to Cite this Article:**Vishvajit Singh, Manju Pruthi, Jagbir Singh, Minimal cyclic codes of length 16p^n over GF(q), where q is prime or prime power of the form 16k+7, J. Math. Comput. Sci., 10 (2020), 1-26 Copyright © 2020 Vishvajit Singh, Manju Pruthi, Jagbir Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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