Construction of isodual codes over GF(q)

Hyun Jin Kim, Yoonjin Lee

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Abstract

We develop a construction method of isodual codes over GF(q), where q is a prime power; we construct isodual codes over GF(q) of length 2n+2 from isodual codes over GF(q) of length 2n. Using this method, we find some isodual codes over GF(q), where q=2,3 and 5. In more detail, we obtain binary isodual codes of lengths 32, 34, 36, 38, and 40, where all these codes of lengths 32, 34, and 36 are optimal and some codes of length 38 are optimal. We note that all these binary isodual codes are not self-dual codes, and in particular, in the case of length 38 all their weight enumerators are different from those of binary self-dual codes of the same length; in fact, four binary isodual codes of length 38 are formally self-dual even codes. We construct isodual codes over GF(3) and GF(5) of lengths 4, 6, and 8 as well.

Original languageEnglish
Pages (from-to)372-385
Number of pages14
JournalFinite Fields and their Applications
Volume45
DOIs
Publication statusPublished - 2017 May 1

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All Science Journal Classification (ASJC) codes

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

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