Self-dual codes over rings and the Chinese remainder theorem

Steven T. Dougherty, Masaaki Harada, Patrick Solé

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

We give some characterizations of self-dual codes over rings, specifically the ring Z2k, where Z2k denotes the ring Z/2kZ of integers modulo 2k, using the Chinese Remainder Theorem, investigating Type I and Type II codes. The Chinese Remainder Theorem plays an important role in the study of self-dual codes over Z2k when 2k is not a prime power, while the Hensel lift is a powerful tool when 2k is a prime power. In particular, we concentrate on the case k = 3 and use construction A to build unimodular and 3-modular lattices.

Original languageEnglish
Pages (from-to)253-283
Number of pages31
JournalHokkaido Mathematical Journal
Volume28
Issue number2
DOIs
Publication statusPublished - 1999
Externally publishedYes

Keywords

  • Codes over rings
  • Self-dual codes
  • Unimodular lattices

ASJC Scopus subject areas

  • Mathematics(all)

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