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

6 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

Bibliographical note

Funding Information:
✩ The authors were supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) founded by the Ministry of Education, Science and Technology (2010-0028298), and the second named author was also supported by the National Research Foundation of Korea (NRF) grant founded by the Korea government (MEST) (No. 2011-0015684). * Corresponding author. E-mail addresses: guswls41@ewha.ac.kr (H.J. Kim), yoonjinl@ewha.ac.kr (Y. Lee).

All Science Journal Classification (ASJC) codes

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

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