Twenty six ternary linear quasi-twisted codes improving the best known lower bounds on minimum distance are constructed.

Sixteen new binary quasi-cyclic linear codes improving the best known lower bounds on minimum distance in Brouwer's tables are constructed. The parameters of these codes are [102, 26, 32], [102, 27, 30], [142, 35, 40], [142, 36, 38] [146, 36, 40], [170, 16, 72], [170, 20, 66], [170, 33, 52] [170, 36, 50], [178, 33, 56], [178, 34, 54], [182, 27, 64] [182, 36, 56], [186, 17, 76], [210, 23, 80], [254, 22, 102] Sixty cyclic and thirty quasi-cyclic codes, which attain the respective bounds in Brouwer's table and are not included in Chen's table are presented as well.

Let [n, k, d]/sub q/-codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF(q). In this article, 31 new quaternary (q=4) codes are constructed which improve the respective lower bounds on minimum distance in Brouwer's tables.

Let [n,k,d;q]-codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF(q). In this correspondence, 18 codes are constructed which improve the known lower bounds on minimum distance.

Let [n,k,d;q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). The following quasi-cyclic codes are constructed in this paper: [44,11,20;3], [55,11:26:3], [66,11,32;3], [48,12,21;3], [60,12,28;3], [56,13,24;3], [65,13,29;3], [56,14,23;3], [60,15,23;3], [64,16,25;3], [36,9,19;4], [90,9,55;4], [99,9,61;4], [30,10,14;4], [50,10,27;4], [55,10,30;4], [33,11,15;4], [44,11,22;4], [55,11,29;4], [36,12,16;4], [48,12,23;4], [60,12,31;4]. All of these codes have established or exceed the respective lower bounds on the minimum distance given by Brouwer.

Let d/sub q/(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 d/sub 4/ (33,5)=22, d/sub 4/(49,5)=34, d/sub 4/(131,5)=96, d/sub 4/(142,5)=104, d/sub 4/(147,5)=108, d/sub 4/(152,5)=112, d/sub 4/(158,5)=116, d/sub 4/(176,5)/spl ges/129, d/sub 4/(180,5)/spl ges/132, d/sub 4/(190,5)/spl ges/140, d/sub 4/(195,5)=144, d/sub 4/(200,5)=148, d/sub 4/(205,5)=152, d/sub 4/(216,5)=160, d/sub 4/(227,5)=168, d/sub 4/(232,5)=172, d/sub 4/(237,5)=176, d/sub 4/(240,5)=178, d/sub 4/(242,5)=180, and d/sub 4/(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 d/sub 4/(n,5) is presented.

Let n/sub 4/(k, d) be the smallest integer n, such that a quaternary linear [n, k, d; 4]-code exists. It is proved that n/sub 4/(5, 20)=30, n/sub 4/(5, 42)/spl ges/59, n/sub 4/(5, 45)/spl ges/63, n/sub 4/(5, 64)/spl ges/88, n/sub 4/(5, 80)=109, n/sub 4/(5, 140)/spl ges/189, n/sub 4/(5, 143)/spl ges/193, n/sub 4/(5, 168)/spl ges/226, n/sub 4/(5, 180)/spl ges/242, n/sub 4/(5, 183)/spl ges/246, n/sub 4/(5, 187)=251.>

Let an (n, k, d)-code denote a binary linear code of length n, dimension k, and minimum distance at least d. Define d(n, k) as the maximum value of d for which there exists a binary linear (n, k, d)-code. T. Verhoeff (1989) has provided an updated table of bounds on d(n, k) for 1>