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

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2 Author(s)
Ran, M. ; Dept. of Electr. Eng.-Syst., Tel Aviv Univ., Israel ; Snyders, J.

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 H 6 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 E4* is applied to construct the Nordstrom-Robinson 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

Published in:

Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 4 )

Date of Publication:

Jul 1996

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