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 journalArticlepeer-review

6 Scopus citations

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
StatePublished - Sep 2012

Keywords

  • 11T71
  • 94B05
  • primary
  • secondary

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