Some cyclic codes of length 8p^n over GF(q), where order of q modulo 8p^n is φ(p^n)/2
Abstract
Let $G$ be a finite group and $F$ be finite field of prime power order $q$ (of type $8k+5$) and order of $q$ modulo $8p^n$ is $\frac{\phi(p^n)}{2}$. If $p$ is prime of type $4k+1$, then the semi-simple ring $R_{8p^n}\equiv \frac{GF(q)[x]}{}$ has $16n+6$ primitive idempotents and for $p$ of type $4k+3$, then $R_{8p^n}$ has $12n+6$ primitive idempotents. The explicit expression for these idempotents are obtained, the generating polynomials and minimum distance bounds for cyclic codes are also completely described.
Copyright © 2019 Jagbir Singh, Sonu 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
J. Singh, S. Singh, Some cyclic codes of length 8p^n over GF(q), where order of q modulo 8p^n is φ(p^n)/2, J. Math. Comput. Sci. 9 (2019), 654–677. https://doi.org/10.28919/jmcs/4201
BibTeX
@article{Singh2019,
author = {Singh, Jagbir and Singh, Sonu},
title = {Some cyclic codes of length 8p^n over GF(q), where order of q modulo 8p^n is φ(p^n)/2},
journal = {J. Math. Comput. Sci.},
volume = {9},
year = {2019},
pages = {654--677},
doi = {10.28919/jmcs/4201}
}