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.
Copyright © 2019 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.
Cite this article
V. Singh, M. Pruthi, J. 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. https://doi.org/10.28919/jmcs/4247
BibTeX
@article{Singh2020,
author = {Singh, Vishvajit and Pruthi, Manju and Singh, Jagbir},
title = {Minimal cyclic codes of length 16p^n over GF(q), where q is prime or prime power of the form 16k+7},
journal = {J. Math. Comput. Sci.},
volume = {10},
year = {2020},
pages = {1--26},
doi = {10.28919/jmcs/4247}
}