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Theoretical study derives primitive idempotents in non-abelian group algebras of order 18, demonstrating new constructions and fundamental parameters for group codes.
Consider the semisimple group algebra F𝒢, where F is a finite field and 𝒢 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 𝒢, 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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Sehrawat et al. (2026) studied this question.
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