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

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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 languageEnglish
Pages (from-to)2148-2157
Number of pages10
JournalDiscrete Mathematics
Volume311
Issue number20
DOIs
Publication statusPublished - 2011 Oct 28
Externally publishedYes

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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