A mass formula for cyclic codes over Galois rings of characteristic p3

Boran Kim; Yoonjin Lee

doi:10.1016/j.ffa.2018.04.005

A mass formula for cyclic codes over Galois rings of characteristic p³

Boran Kim, Yoonjin Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We completely determine the explicit generators of cyclic codes of length p^k(k≥1) over a Galois ring of characteristic p³ by their residue degree, and their two torsional degrees; there are exactly three types of cyclic codes, that is, one-generator, two-generator and three-generator cyclic codes. Using this classification result, we explicitly obtain a mass formula for cyclic codes of length p^k over a Galois ring of characteristic p³.

Original language	English
Pages (from-to)	214-242
Number of pages	29
Journal	Finite Fields and their Applications
Volume	52
DOIs	https://doi.org/10.1016/j.ffa.2018.04.005
State	Published - Jul 2018

Bibliographical note

Funding Information:
Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2017R1A2B2004574). The authors are also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).

Publisher Copyright:
© 2018

Keywords

Cyclic code
Galois ring
Generator
Ideal
Mass formula

Access to Document

10.1016/j.ffa.2018.04.005

Cite this

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title = "A mass formula for cyclic codes over Galois rings of characteristic p3 ",

abstract = "We completely determine the explicit generators of cyclic codes of length pk(k≥1) over a Galois ring of characteristic p3 by their residue degree, and their two torsional degrees; there are exactly three types of cyclic codes, that is, one-generator, two-generator and three-generator cyclic codes. Using this classification result, we explicitly obtain a mass formula for cyclic codes of length pk over a Galois ring of characteristic p3.",

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AU - Lee, Yoonjin

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N2 - We completely determine the explicit generators of cyclic codes of length pk(k≥1) over a Galois ring of characteristic p3 by their residue degree, and their two torsional degrees; there are exactly three types of cyclic codes, that is, one-generator, two-generator and three-generator cyclic codes. Using this classification result, we explicitly obtain a mass formula for cyclic codes of length pk over a Galois ring of characteristic p3.

AB - We completely determine the explicit generators of cyclic codes of length pk(k≥1) over a Galois ring of characteristic p3 by their residue degree, and their two torsional degrees; there are exactly three types of cyclic codes, that is, one-generator, two-generator and three-generator cyclic codes. Using this classification result, we explicitly obtain a mass formula for cyclic codes of length pk over a Galois ring of characteristic p3.

KW - Cyclic code

KW - Galois ring

KW - Generator

KW - Ideal

KW - Mass formula

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