Optimal self-dual Z 4-codes and a unimodular lattice in dimension 41

Masaaki Harada

doi:10.1016/j.ffa.2011.11.004

Optimal self-dual Z ₄-codes and a unimodular lattice in dimension 41

Masaaki Harada

INF - System Information Sciences

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

1 Citation (Scopus)

Abstract

For lengths up to 47 except 37, we determine the largest minimum Euclidean weight among all Type I Z ₄-codes of that length. We also give the first example of an optimal odd unimodular lattice in dimension 41 explicitly, which is constructed from some Type I Z ₄-code of length 41.

Original language	English
Pages (from-to)	529-536
Number of pages	8
Journal	Finite Fields and Their Applications
Volume	18
Issue number	3
DOIs	https://doi.org/10.1016/j.ffa.2011.11.004
Publication status	Published - 2012 May

Keywords

Doubly even code
Extremal code
Self-dual code
Unimodular lattice

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10.1016/j.ffa.2011.11.004

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title = "Optimal self-dual Z 4-codes and a unimodular lattice in dimension 41",

abstract = "For lengths up to 47 except 37, we determine the largest minimum Euclidean weight among all Type I Z 4-codes of that length. We also give the first example of an optimal odd unimodular lattice in dimension 41 explicitly, which is constructed from some Type I Z 4-code of length 41.",

keywords = "Doubly even code, Extremal code, Self-dual code, Unimodular lattice",

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N2 - For lengths up to 47 except 37, we determine the largest minimum Euclidean weight among all Type I Z 4-codes of that length. We also give the first example of an optimal odd unimodular lattice in dimension 41 explicitly, which is constructed from some Type I Z 4-code of length 41.

AB - For lengths up to 47 except 37, we determine the largest minimum Euclidean weight among all Type I Z 4-codes of that length. We also give the first example of an optimal odd unimodular lattice in dimension 41 explicitly, which is constructed from some Type I Z 4-code of length 41.

KW - Doubly even code

KW - Extremal code

KW - Self-dual code

KW - Unimodular lattice

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JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

IS - 3

ER -

Optimal self-dual Z ₄-codes and a unimodular lattice in dimension 41

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Keywords

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