A mass formula for cyclic codes over Galois rings of characteristic p3

Boran Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We completely determine the explicit generators of cyclic codes of length pk(k≥1) over a Galois ring of characteristic p3 by their residue degree, and their two torsional degrees; there are exactly three types of cyclic codes, that is, one-generator, two-generator and three-generator cyclic codes. Using this classification result, we explicitly obtain a mass formula for cyclic codes of length pk over a Galois ring of characteristic p3.

Original languageEnglish
Pages (from-to)214-242
Number of pages29
JournalFinite Fields and their Applications
Volume52
DOIs
StatePublished - Jul 2018

Keywords

  • Cyclic code
  • Galois ring
  • Generator
  • Ideal
  • Mass formula

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