Cyclic codes of length $ 2p^n $ over finite chain rings

Anderson Silva; C. Polcino Milies

doi:10.3934/amc.2020017

Article Contents

2020, Volume 14, Issue 2: 233-245. Doi: 10.3934/amc.2020017

This issue Previous Article Efficient traceable ring signature scheme without pairings Next Article Constructing 1-resilient rotation symmetric functions over

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variables through special orthogonal arrays

Cyclic codes of length $ 2p^n $ over finite chain rings

Anderson Silva^1, and
C. Polcino Milies^2,

1.
Departamento de Matemática, Universidade Federal de Viçosa, Viçosa, 36570-000, Brazil
2.
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, 05311-970, Brazil

Received: January 31, 2018

Revised: February 28, 2019

Early access: September 2019

Published: May 2020

This work was partially supported by CNPq., Proc. 300243/79-0(RN) and FAPESP, Proc 2015/09162-9

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Abstract

We use group algebra methods to study cyclic codes over finite chain rings and under some restrictive hypotheses, described in section 2, for codes of length $ 2p^n $, $ p $ a prime, we are able to compute the minimum weights of all possible cyclic codes of that length.

Keywords:

Cyclic codes,
chain rings,
weights.

Mathematics Subject Classification: Primary: 94B15, 06F25, 20C05; Secondary: 94A05, 94B05.

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References

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