Finite quasi-Frobenius modules and linear codes

Marcus Greferath*, Alexandr Nechaev, Robert Wisbauer

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The theory of linear codes over finite fields has been extended by A. Nechaev to codes over quasi-Frobenius modules over commutative rings, and by J. Wood to codes over (not necessarily commutative) finite Frobenius rings. In the present paper, we subsume these results by studying linear codes over quasi-Frobenius and Frobenius modules over any finite ring. Using the character module of the ring as alphabet, we show that fundamental results like MacWilliams' theorems on weight enumerators and code isometry can be obtained in this general setting.

Original languageEnglish
Pages (from-to)247-272
Number of pages26
JournalJOURNAL OF ALGEBRA AND ITS APPLICATIONS
Volume3
Issue number3
DOIs
Publication statusPublished - Sep 2004
MoE publication typeA1 Journal article-refereed

Keywords

  • (quasi) Frobenius module
  • symmetric ring
  • homogeneous function
  • linear code over a module
  • McWilliams' theorems

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