On equivalence of cyclic and dihedral zero-divisor codes having nilpotents of nilpotency degree two as generators

Kai Lin Ong, Miin Huey Ang

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Abstract

Zero-divisor codes are codes constructed using group rings where their generators are zero-divisors. Generally, zero-divisor codes can be equivalent despite their associated groups are non-isomorphic, leading to the proposed conjecture “Every dihedral zero-divisor code has an equivalent form of cyclic zero-divisor code”. This paper is devoted to study equivalence of zero-divisor codes in F2G having generators from the 2-nilradical of F2G, consisting of all nilpotents of nilpotency degree 2 of F2G. Essentially, algebraic structures of 2-nilradicals are first studied in general for both commutative and non-commutative F2G before specialized into the case when G is cyclic and dihedral. Then, results are used to study the conjecture above in the cases where the codes generators are from their respective 2-nilradicals.
Original languageEnglish
Pages (from-to)1127-1138
Number of pages12
JournalDesigns, Codes and Cryptography
Volume90
Issue number5
Early online date22 Mar 2022
DOIs
Publication statusPublished - May 2022

Keywords

  • Code equivalence
  • Group ring codes
  • Nilpotents
  • Zero-divisor codes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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