On the residue codes of extremal Type II ℤ 4-codes of lengths 32 and 40

Masaaki Harada

doi:10.1016/j.disc.2011.06.022

On the residue codes of extremal Type II ℤ ₄-codes of lengths 32 and 40

Masaaki Harada

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

In this paper, we determine the dimensions of the residue codes of extremal Type II ^Z4-codes of lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some extremal Type II ^Z4-code. It is also shown that there is a unique extremal Type II ^Z4-code of length 32 whose residue code has the smallest dimension 6 up to equivalence. As a consequence, many new extremal Type II ^Z4-codes of lengths 32 and 40 are constructed.

Original language	English
Pages (from-to)	2148-2157
Number of pages	10
Journal	Discrete Mathematics
Volume	311
Issue number	20
DOIs	https://doi.org/10.1016/j.disc.2011.06.022
Publication status	Published - 2011 Oct 28
Externally published	Yes

Keywords

Binary doubly even code
Extremal Type II -code
Residue code

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2011.06.022

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Harada, M. (2011). On the residue codes of extremal Type II ℤ ₄-codes of lengths 32 and 40. Discrete Mathematics, 311(20), 2148-2157. https://doi.org/10.1016/j.disc.2011.06.022

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