Expression for primitive idempotents of length 8pn and corresponding codes
Abstract
The group algebra FG of the group G of order 8pn over the field F of prime power order q, where p is an odd prime n≥1, q is of the form 8k+1 and q is primitive root modulo pn, have 8(n+1) primitive idempotents. The explicit expressions for these idempotents are obtained. Generating polynomials, minimum distances and dimensions for the corresponding minimal cyclic codes are also obtained.
Copyright © 2022 Jagbir Singh, Sonika Ahlawat, S.K. Arora. 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. Ahlawat, S. K. Arora, Expression for primitive idempotents of length 8pn and corresponding codes, J. Math. Comput. Sci. 12 (2022), 139. https://doi.org/10.28919/jmcs/7299
BibTeX
@article{Singh2022,
author = {Singh, Jagbir and Ahlawat, Sonika and Arora, S.K.},
title = {Expression for primitive idempotents of length 8pn and corresponding codes},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {139},
doi = {10.28919/jmcs/7299}
}