Construction of extremal self-dual codes over Z8 and Z16

Boran Kim; Yoonjin Lee

doi:10.1007/s10623-015-0137-8

Construction of extremal self-dual codes over Z₈ and Z₁₆

Boran Kim
, Yoonjin Lee

Department of Mathematics Education

Ewha Womans University

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

4 Scopus citations

Abstract

We present a method of constructing free self-dual codes over Z₈ and Z₁₆ which are extremal or optimal with respect to the Hamming weight. We first prove that every (extremal or optimal) free self-dual code over Z2m can be found from a binary (extremal or optimal) Type II code for any positive integer m≥ 2. We find explicit algorithms for construction of self-dual codes over Z₈ and Z₁₆. Our construction method is basically a lifting method. Furthermore, we find an upper bound of minimum Hamming weights of free self-dual codes over Z2m. By using our explicit algorithms, we construct extremal free self-dual codes over Z₈ and Z₁₆ up to lengths 40.

Original language	English
Pages (from-to)	239-257
Number of pages	19
Journal	Designs, Codes, and Cryptography
Volume	81
Issue number	2
DOIs	https://doi.org/10.1007/s10623-015-0137-8
State	Published - 1 Nov 2016

Keywords

Code over a ring
Extremal self-dual code
Free self-dual code
Optimal self-dual code
Self-dual code

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10.1007/s10623-015-0137-8

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title = "Construction of extremal self-dual codes over Z8 and Z16 ",

abstract = "We present a method of constructing free self-dual codes over Z8 and Z16 which are extremal or optimal with respect to the Hamming weight. We first prove that every (extremal or optimal) free self-dual code over Z2m can be found from a binary (extremal or optimal) Type II code for any positive integer m≥ 2. We find explicit algorithms for construction of self-dual codes over Z8 and Z16. Our construction method is basically a lifting method. Furthermore, we find an upper bound of minimum Hamming weights of free self-dual codes over Z2m. By using our explicit algorithms, we construct extremal free self-dual codes over Z8 and Z16 up to lengths 40.",

keywords = "Code over a ring, Extremal self-dual code, Free self-dual code, Optimal self-dual code, Self-dual code",

author = "Boran Kim and Yoonjin Lee",

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AU - Lee, Yoonjin

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AB - We present a method of constructing free self-dual codes over Z8 and Z16 which are extremal or optimal with respect to the Hamming weight. We first prove that every (extremal or optimal) free self-dual code over Z2m can be found from a binary (extremal or optimal) Type II code for any positive integer m≥ 2. We find explicit algorithms for construction of self-dual codes over Z8 and Z16. Our construction method is basically a lifting method. Furthermore, we find an upper bound of minimum Hamming weights of free self-dual codes over Z2m. By using our explicit algorithms, we construct extremal free self-dual codes over Z8 and Z16 up to lengths 40.

KW - Code over a ring

KW - Extremal self-dual code

KW - Free self-dual code

KW - Optimal self-dual code

KW - Self-dual code

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SN - 0925-1022

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JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 2

ER -

Construction of extremal self-dual codes over Z₈ and Z₁₆

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