Hermitian self-dual codes over F 2 2m + uF22m

Hyun Jin Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We present a method for construction of Hermitian self-dual codes over F2 2m + uF22m from Hermitian self-dual codes over F 22m via a Gray map we define, where m is a positive integer. For constructing self-dual codes over F2+uF2 with an automorphism of odd order using the decomposition theory, it is necessary to find Hermitian self-dual codes over F22m+uF22m for some appropriate positive integer m. Using the Gray map, we show how to check the equivalence of codes over F2 2m+uF22m from the information on the equivalence of codes over F2 2m. We thus classify all Hermitian self-dual codes over F22+uF22 of lengths up to 8. Using these codes, we complete the classification of the Lee-extremal self-dual codes over F2+uF2 of lengths 21 and 22 with a nontrivial automorphism of odd order; these were open cases in the authors' previous work [10].

Original languageEnglish
Pages (from-to)106-131
Number of pages26
JournalFinite Fields and their Applications
Volume25
DOIs
StatePublished - 2014

Keywords

  • Gray map
  • Self-dual code

Fingerprint

Dive into the research topics of 'Hermitian self-dual codes over F 2 2m + uF22m'. Together they form a unique fingerprint.

Cite this