A cyclic [6,3,4] group code and the hexacode over GF(4)

Moshe Ran*, Jakov Snyders

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A [6,3,4] code E6 over an Abelian group A4 with four elements is presented. E6 is cyclic, unlike the [6,3,4] hexacode H6 over GF(4) However, E6 and H6, are isomorphic when the latter is viewed as a group code. Differences and similarities between E6 and H6 are discussed. A dual code of E6 is presented. Some binary codes, among them the [24,12,8]Golay, are derived with the aid of E6. A related cyclic [4,2,3] code E*4 is applied to construct the Nordstrom-Rohinson code. E6 is the smallest member of a class of [2k, k, 4] cyclic and reversible codes over A4. Another class of cyclic and reversible codes of length 2ℓ + 1 ; ℓ ≥ 2 and minimum distance 3 over A4 is also presented.

Original languageEnglish
Pages (from-to)1250-1253
Number of pages4
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - 1996


  • Binary image
  • Cyclic code
  • Elementary Abelian group
  • Group code
  • Hcxacode


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