An upper bound on the minimum weight of Type II Z2k-codes

Masaaki Harada; Tsuyoshi Miezaki

doi:10.1016/j.jcta.2010.02.007

An upper bound on the minimum weight of Type II Z_2k-codes

Masaaki Harada^*, Tsuyoshi Miezaki

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

In this paper, we give a new upper bound on the minimum Euclidean weight of Type II Z_2k-codes and the concept of extremality for the Euclidean weights when k=3,4,5,6. Together with the known result, we demonstrate that there is an extremal Type II Z_2k-code of length 8. m (m≤8) when k=3,4,5,6.

Original language	English
Pages (from-to)	190-196
Number of pages	7
Journal	Journal of Combinatorial Theory. Series A
Volume	118
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2010.02.007
Publication status	Published - 2011 Jan
Externally published	Yes

Keywords

Euclidean weight
Extremal code
Theta series
Type II code

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1016/j.jcta.2010.02.007

Cite this

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title = "An upper bound on the minimum weight of Type II Z2k-codes",

abstract = "In this paper, we give a new upper bound on the minimum Euclidean weight of Type II Z2k-codes and the concept of extremality for the Euclidean weights when k=3,4,5,6. Together with the known result, we demonstrate that there is an extremal Type II Z2k-code of length 8. m (m≤8) when k=3,4,5,6.",

keywords = "Euclidean weight, Extremal code, Theta series, Type II code",

author = "Masaaki Harada and Tsuyoshi Miezaki",

note = "Funding Information: E-mail addresses: mharada@sci.kj.yamagata-u.ac.jp (M. Harada), miezaki@math.sci.hokudai.ac.jp (T. Miezaki). 1 This work was partially supported by JSPS KAKENHI (20540103).",

year = "2011",

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AU - Harada, Masaaki

AU - Miezaki, Tsuyoshi

N1 - Funding Information: E-mail addresses: mharada@sci.kj.yamagata-u.ac.jp (M. Harada), miezaki@math.sci.hokudai.ac.jp (T. Miezaki). 1 This work was partially supported by JSPS KAKENHI (20540103).

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N2 - In this paper, we give a new upper bound on the minimum Euclidean weight of Type II Z2k-codes and the concept of extremality for the Euclidean weights when k=3,4,5,6. Together with the known result, we demonstrate that there is an extremal Type II Z2k-code of length 8. m (m≤8) when k=3,4,5,6.

AB - In this paper, we give a new upper bound on the minimum Euclidean weight of Type II Z2k-codes and the concept of extremality for the Euclidean weights when k=3,4,5,6. Together with the known result, we demonstrate that there is an extremal Type II Z2k-code of length 8. m (m≤8) when k=3,4,5,6.

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KW - Extremal code

KW - Theta series

KW - Type II code

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