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

Hyun Jin Kim, Yoonjin Lee

Research output: Contribution to journalArticle

2 Citations (Scopus)

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
Publication statusPublished - 2014 Jan 1

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Self-dual Codes
Gray Map
Decomposition
Automorphism
Odd
Extremal Codes
Equivalence
Integer
Classify
Decompose
Necessary

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

Cite this

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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].",
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Hermitian self-dual codes over F 2 2m + uF22m. / Kim, Hyun Jin; Lee, Yoonjin.

In: Finite Fields and their Applications, Vol. 25, 01.01.2014, p. 106-131.

Research output: Contribution to journalArticle

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