Construction of extremal self-dual codes over F 2uF 2 with an automorphism of odd order

Hyun Jin Kim, Yoonjin Lee

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We complete the classification the Lee-extremal self-dual codes over the ring F 2uF 2 of lengths 21 and 22 with a nontrivial automorphism of odd prime order except the case for an automorphism of order 3 with seven cycles, and we partially classify the exceptional case. In particular, we show that there are 138 (respectively, 6723) inequivalent Lee-extremal self-dual codes of length 21 (respectively, 22) with an automorphism of odd prime order. We use the decomposition theory for self-dual codes over F 2uF 2 with an automorphism of odd prime order as the same approaches made by Huffman. And we also use an extension method as a new approach, and the current approach is extending the even subcode part while the fixed subcode part is extended in the authors previous work.

Original languageEnglish
Pages (from-to)971-992
Number of pages22
JournalFinite Fields and their Applications
Volume18
Issue number5
DOIs
Publication statusPublished - 2012 Sep 1

Fingerprint

Extremal Codes
Self-dual Codes
Automorphism
Odd
Decomposition
Classify
Ring
Cycle
Decompose

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 complete the classification the Lee-extremal self-dual codes over the ring F 2uF 2 of lengths 21 and 22 with a nontrivial automorphism of odd prime order except the case for an automorphism of order 3 with seven cycles, and we partially classify the exceptional case. In particular, we show that there are 138 (respectively, 6723) inequivalent Lee-extremal self-dual codes of length 21 (respectively, 22) with an automorphism of odd prime order. We use the decomposition theory for self-dual codes over F 2uF 2 with an automorphism of odd prime order as the same approaches made by Huffman. And we also use an extension method as a new approach, and the current approach is extending the even subcode part while the fixed subcode part is extended in the authors previous work.",
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Construction of extremal self-dual codes over F 2uF 2 with an automorphism of odd order. / Kim, Hyun Jin; Lee, Yoonjin.

In: Finite Fields and their Applications, Vol. 18, No. 5, 01.09.2012, p. 971-992.

Research output: Contribution to journalArticle

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