Construction of extremal Type II Z2k-codes

Masaaki Harada

doi:10.1016/j.ffa.2022.102154

Construction of extremal Type II Z_2k-codes

Masaaki Harada

INF - System Information Sciences

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

Abstract

We give methods for constructing many self-dual Z_m-codes and Type II Z_2k-codes of length 2n starting from a given self-dual Z_m-code and Type II Z_2k-code of length 2n, respectively. As an application, we construct extremal Type II Z_2k-codes of length 24 for k=4,5,…,20 and extremal Type II Z_2k-codes of length 32 for k=4,5,…,10. We also construct new extremal Type II Z₄-codes of lengths 56 and 64.

Original language	English
Article number	102154
Journal	Finite Fields and their Applications
Volume	87
DOIs	https://doi.org/10.1016/j.ffa.2022.102154
Publication status	Published - 2023 Mar

Keywords

Extremal Type II code
Self-dual code
Type II code

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
Engineering(all)
Applied Mathematics

Access to Document

10.1016/j.ffa.2022.102154

Cite this

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title = "Construction of extremal Type II Z2k-codes",

abstract = "We give methods for constructing many self-dual Zm-codes and Type II Z2k-codes of length 2n starting from a given self-dual Zm-code and Type II Z2k-code of length 2n, respectively. As an application, we construct extremal Type II Z2k-codes of length 24 for k=4,5,…,20 and extremal Type II Z2k-codes of length 32 for k=4,5,…,10. We also construct new extremal Type II Z4-codes of lengths 56 and 64.",

keywords = "Extremal Type II code, Self-dual code, Type II code",

author = "Masaaki Harada",

note = "Funding Information: This work was supported by JSPS KAKENHI Grant Number 19H01802 . The author would like to thank the anonymous reviewers for useful comments. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2023",

month = mar,

doi = "10.1016/j.ffa.2022.102154",

language = "English",

volume = "87",

journal = "Finite Fields and Their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

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AU - Harada, Masaaki

N1 - Funding Information: This work was supported by JSPS KAKENHI Grant Number 19H01802 . The author would like to thank the anonymous reviewers for useful comments. Publisher Copyright: © 2022 Elsevier Inc.

PY - 2023/3

Y1 - 2023/3

N2 - We give methods for constructing many self-dual Zm-codes and Type II Z2k-codes of length 2n starting from a given self-dual Zm-code and Type II Z2k-code of length 2n, respectively. As an application, we construct extremal Type II Z2k-codes of length 24 for k=4,5,…,20 and extremal Type II Z2k-codes of length 32 for k=4,5,…,10. We also construct new extremal Type II Z4-codes of lengths 56 and 64.

AB - We give methods for constructing many self-dual Zm-codes and Type II Z2k-codes of length 2n starting from a given self-dual Zm-code and Type II Z2k-code of length 2n, respectively. As an application, we construct extremal Type II Z2k-codes of length 24 for k=4,5,…,20 and extremal Type II Z2k-codes of length 32 for k=4,5,…,10. We also construct new extremal Type II Z4-codes of lengths 56 and 64.

KW - Extremal Type II code

KW - Self-dual code

KW - Type II code

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