Session S29 - Theory and Applications of Coding Theory

Tuesday, July 13, 15:30 ~ 15:55 UTC-3

Essential idempotents and Nilpotent Group Codes

César Polcino Milies

Universidade de São Paulo, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We recall the definition of essential idempotents and its implications for cyclic and Abelian codes. Then, we consider nilpotent group codes, i.e. codes that can be realized as ideals in the finite (semisimple) group algebra of a nilpotent group. We discuss the existence of essential idempotents in this context and study properties of minimal nilpotent codes.

References [1] G.Chalom, R. Ferraz and C.Polcino Milies, Essential idempotents and simplex codes, J. Algebra, Discrete Structures and Appl., 4, 2 (2017), 181-188. [2] G.Chalom, R. Ferraz and C.Polcino Milies, Essencial idempotents and codes of constant weight, Sâo Paulo J. of Math. Sci,, 11 (2) (2018), 253-260 [3] A. Duarte, On nilpotent and constacyclic codes, tese de doutoramento, Universidade Federal do ABC, Santo André, Brazil, 2021.

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