A cyclic [6,3,4] group code and the hexacode over GF(4)
1996; Institute of Electrical and Electronics Engineers; Volume: 42; Issue: 4 Linguagem: Inglês
10.1109/18.508851
ISSN1557-9654
Autores Tópico(s)graph theory and CDMA systems
ResumoA [6,3,4] code E/sub 6/ over an Abelian group A/sub 4/ with four elements is presented. E/sub 6/ is cyclic, unlike the [6,3,4] hexacode H/sub 6/ over GF(4). However, E/sub 6/ and H/sub 6/ are isomorphic when the latter is viewed as a group code. Differences and similarities between E/sub 6/ and H/sub 6/ are discussed. A dual code of E/sub 6/ is presented. Some binary codes, among them the [24,12,8] Golay, are derived with the aid of E/sub 6/. A related cyclic [4,2,3] code E/sub 4/* is applied to construct the Nordstrom-Robinson code. E/sub 6/ is the smallest member of a class of [2k,k,4] cyclic and reversible codes over A/sub 4/. Another class of cyclic and reversible codes of length 2l+1; l/spl ges/2 and minimum distance 3 over A/sub 4/ is also presented.
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