Explicit idempotents of finite group algebras.

DOI10.1016/j.ffa.2014.02.002zbMath1298.20004arXiv1404.6009OpenAlexW3103355403MaRDI QIDQ402552

Carmen Rosa Giraldo Vergara, Fabio Enrique Brochero Martínez

Publication date: 28 August 2014

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.6009

zbMATH Keywords

group algebrasprimitive idempotentsfinite cyclic \(p\)-groupsirreducible cyclic codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Cyclic codes (94B15)

Related Items (5)

Idempotents of generalized quaternion group algebras and their applications ⋮ LCD codes and self-orthogonal codes in generalized dihedral group algebras ⋮ Structure of finite dihedral group algebra. ⋮ LCD codes and self-orthogonal codes in finite dihedral group algebras ⋮ Left ideals of matrix rings and error-correcting codes

Cites Work

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• Idempotents in group algebras and minimal abelian codes
• Minimal codes of prime-power length.
• Minimal cyclic codes of length \(2p^n\)
• Factorization of the cyclotomic polynomial \(x^{2^n}+1\) over finite fields
• Cyclotomic numbers and primitive idempotents in the ring \(\mathrm{GF}(q)[x/(x^{p^n} - 1)\)]
• Explicit Factorizations of Cyclotomic and Dickson Polynomials over Finite Fields

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