Essential idempotents and simplex codes

Year 2017, Volume: 4 Issue: 2 (Special Issue: Noncommutative rings and their applications), 181 - 188, 10.01.2017

Gladys Chalom Raul A. Ferraz , Cesar Polcino Milies

https://doi.org/10.13069/jacodesmath.284931

Cited By: 4

Abstract

We define essential idempotents in group algebras and use them to prove that every mininmal abelian non-cyclic code is a repetition code. Also we use them to prove that every minimal abelian code is equivalent to a minimal cyclic code of the same length. Finally, we show that a binary cyclic code is simplex if and only if is of length of the form $n=2^k-1$ and is generated by an essential idempotent.

Keywords

Group code , Essential idempotent , Simplex code

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