Codes of length 18 over Non-Abelian Groups

Consider the semisimple group algebra F๐’ข, where F is a finite field and ๐’ข is a non-abelian group of order 18. In this paper, we derive both linear and non-linear primitive idempotents by utilizing the character theory of ๐’ข, and these idempotents are used to construct a family of group codes. Furthermore, we determine fundamental parameters of these group codes.

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Publication Details

Journal
Galois Journal of Algebra
Published
2026-09-05
DOI
https://doi.org/10.65908/gja.2026.8489.1038
Primary Topic
Coding theory and cryptography
Type
article
Field-Weighted Citation Impact
0.00
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article

Codes of length 18 over Non-Abelian Groups

Manju Pruthi, Sudesh Sehrawat
Galois Journal of Algebra
Coding theory and cryptography
article

Codes of length 18 over Non-Abelian Groups

Manju Pruthi, Sudesh Sehrawat
article en

Abstract

Consider the semisimple group algebra F๐’ข, where F is a finite field and ๐’ข is a non-abelian group of order 18. In this paper, we derive both linear and non-linear primitive idempotents by utilizing the character theory of ๐’ข, and these idempotents are used to construct a family of group codes. Furthermore, we determine fundamental parameters of these group codes.

Galois Journal of Algebra
Shree Guru Gobind Singh Tricentenary University (IN), Indira Gandhi Mirpur University (IN)
Openalex Percentile: Top 8%
Coding theory and cryptography
DOIOpen Access PDFOpenAlex
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