@article{article_284931, title={Essential idempotents and simplex codes}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={4}, pages={181–188}, year={2017}, DOI={10.13069/jacodesmath.284931}, author={Chalom, Gladys and Ferraz, Raul A. and Milies, Cesar Polcino}, keywords={Group code,Essential idempotent,Simplex code}, 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.}, number={2 (Special Issue: Noncommutative rings and their applications)}, publisher={iPeak Academy}