On rank and Kernel of ℤ4-linear codes

Cristina Fernández-Córdoba*, Jaume Pujol, Mercè Villanueva

*Corresponding author for this work

Research output: Chapter in BookChapterResearchpeer-review

5 Citations (Scopus)

Abstract

A code is a quaternary linear code if is a subgroup of ℤ4. In this paper, the rank and dimension of the kernel for ℤ4- linear codes, which are the corresponding binary codes of quaternary linear codes, are studied. The possible values of these two parameters for ℤ4-linear codes, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a ℤ4-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a ℤ4- linear code with dimension of the kernel k is given.

Original languageEnglish
Title of host publicationCoding Theory and Applications - Second International Castle Meeting, ICMCTA 2008, Proceedings
Pages46-55
Number of pages10
DOIs
Publication statusPublished - 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5228 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • ℤ-linear codes
  • Kernel
  • Quaternary codes
  • Rank

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