Parity check systems of nonlinear codes over finite commutative frobenius rings

Thomas Westerbäck*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The concept of parity check matrices of linear binary codes has been extended by Heden [10] to parity check systems of nonlinear binary codes. In the present paper we extend this concept to parity check systems of nonlinear codes over finite commutative Frobenius rings. Using parity check systems, results on how to get some fundamental properties of the codes are given. Moreover, parity check systems and its connection to characters is investigated and a MacWilliams type theorem on the distance distribution is given.

Original languageEnglish
Pages (from-to)409-427
Number of pages19
JournalAdvances in Mathematics of Communications
Volume11
Issue number3
DOIs
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Characters
  • Discrete fourier analysis
  • Finite commutative frobenius rings
  • MacWilliams type theorem
  • Nonlinear codes
  • Parity check systems

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