Title :
A cyclic [6,3,4] group code and the hexacode over GF(4)
Author :
Ran, Moshe ; Snyders, Jakov
Author_Institution :
Dept. of Electr. Eng.-Syst., Tel Aviv Univ., Israel
fDate :
7/1/1996 12:00:00 AM
Abstract :
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
Keywords :
Galois fields; binary sequences; cyclic codes; dual codes; Abelian group; Golay code; Nordstrom-Robinson code; binary codes; code length; cyclic group code; dual code; hexacode; minimum code distance; reversible codes; Additives; Binary codes; Conferences; Galois fields; Hamming distance; Helium; Linear code; Mercury (metals); Modulation coding; Radio access networks;
Journal_Title :
Information Theory, IEEE Transactions on
