Lee weights of cyclic self-dual codes over Galois rings of characteristic p2

Boran Kim; Yoonjin Lee

doi:10.1016/j.ffa.2016.11.015

Lee weights of cyclic self-dual codes over Galois rings of characteristic p²

Boran Kim, Yoonjin Lee

Department of Mathematics Education

Ewha Womans University

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

14 Scopus citations

Abstract

We completely determine the minimum Lee weights of cyclic self-dual codes over a Galois ring GR(p²,m) of length p^k, where m and k are positive integers and p is a prime number. We obtain all cyclic self-dual codes over GR(2²,1)≅Z₄ of lengths 16 and 32 with their Lee weight enumerators. We also find cyclic self-dual codes over GR(3²,1)≅Z₉ (respectively, GR(3²,2)) of lengths up to 27 (respectively, 9). Most of the cyclic self-dual codes we found are extremal with respect to the Lee weights.

Original language	English
Pages (from-to)	107-130
Number of pages	24
Journal	Finite Fields and their Applications
Volume	45
DOIs	https://doi.org/10.1016/j.ffa.2016.11.015
State	Published - 1 May 2017

Keywords

Cyclic code
Extremal code
Galois ring
Minimum Lee weight
Self-dual code

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10.1016/j.ffa.2016.11.015

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title = "Lee weights of cyclic self-dual codes over Galois rings of characteristic p2",

abstract = "We completely determine the minimum Lee weights of cyclic self-dual codes over a Galois ring GR(p2,m) of length pk, where m and k are positive integers and p is a prime number. We obtain all cyclic self-dual codes over GR(22,1)≅Z4 of lengths 16 and 32 with their Lee weight enumerators. We also find cyclic self-dual codes over GR(32,1)≅Z9 (respectively, GR(32,2)) of lengths up to 27 (respectively, 9). Most of the cyclic self-dual codes we found are extremal with respect to the Lee weights.",

keywords = "Cyclic code, Extremal code, Galois ring, Minimum Lee weight, Self-dual code",

author = "Boran Kim and Yoonjin Lee",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

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doi = "10.1016/j.ffa.2016.11.015",

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AU - Kim, Boran

AU - Lee, Yoonjin

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We completely determine the minimum Lee weights of cyclic self-dual codes over a Galois ring GR(p2,m) of length pk, where m and k are positive integers and p is a prime number. We obtain all cyclic self-dual codes over GR(22,1)≅Z4 of lengths 16 and 32 with their Lee weight enumerators. We also find cyclic self-dual codes over GR(32,1)≅Z9 (respectively, GR(32,2)) of lengths up to 27 (respectively, 9). Most of the cyclic self-dual codes we found are extremal with respect to the Lee weights.

AB - We completely determine the minimum Lee weights of cyclic self-dual codes over a Galois ring GR(p2,m) of length pk, where m and k are positive integers and p is a prime number. We obtain all cyclic self-dual codes over GR(22,1)≅Z4 of lengths 16 and 32 with their Lee weight enumerators. We also find cyclic self-dual codes over GR(32,1)≅Z9 (respectively, GR(32,2)) of lengths up to 27 (respectively, 9). Most of the cyclic self-dual codes we found are extremal with respect to the Lee weights.

KW - Cyclic code

KW - Extremal code

KW - Galois ring

KW - Minimum Lee weight

KW - Self-dual code

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DO - 10.1016/j.ffa.2016.11.015

M3 - Article

AN - SCOPUS:85008420054

SN - 1071-5797

VL - 45

SP - 107

EP - 130

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Lee weights of cyclic self-dual codes over Galois rings of characteristic p²

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Keywords

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