Abstract :
Let dq(n,k) be the maximum possible minimum Hamming distance of a q-ary [n,k,d]-code for given values of n and k. It is proved that d4 (33,5)=22, d4(49,5)=34, d4 (131,5)=96, d4(142,5)=104, d4(147,5)=108, d 4(152,5)=112, d4(158,5)=116, d4(176,5)⩾129, d4(180,5)⩾132, d4(190,5)⩾140, d4(195,5)=144, d4(200,5)=148, d4(205,5)=152, d4(216,5)=160, d4(227,5)=168, d4(232,5)=172, d4(237,5)=176, d4(240,5)=178, d4(242,5)=180, and d4(247,5)=184. A survey of the results of recent work on bounds for quaternary linear codes in dimensions four and five is made and a table with lower and upper bounds for d4(n,5) is presented
Keywords :
Galois fields; linear codes; dimension five; lower bounds; maximum possible minimum Hamming distance; optimal quaternary linear codes; q-ary [n,k,d]-code; upper bounds; Conferences; Galois fields; Hamming distance; Linear code; Upper bound; Vectors;
