TY  - JOUR
TT  - Essential idempotents and simplex codes
AU  - Chalom, Gladys
AU  - Ferraz, Raul A.
AU  - Milies, Cesar Polcino
PY  - 2017
DA  - May
DO  - 10.13069/jacodesmath.284931
JF  - Journal of Algebra Combinatorics Discrete Structures and Applications
PB  - iPeak Academy
WT  - DergiPark
SN  - 2148-838X
SP  - 181
EP  - 188
VL  - 4
IS  - 2 (Special Issue: Noncommutative rings  and  their applications)
KW  - Group code
KW  - Essential idempotent
KW  - Simplex code
N2  - 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.
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UR  - https://doi.org/10.13069/jacodesmath.284931
L1  - https://dergipark.org.tr/en/download/article-file/267223
ER  -