A covering code construction is presented. Using this construction it is shown that t[52,39]=3, t[36,21]=4, t[58,32]=7, K(32,2)/spl les/62/spl middot/2/sup 18/, and K(62,5)/spl les/31/spl middot/2/sup 37/, where t[n,k] is the minimum covering radius among all binary [n,k] codes and K(n,R) is the minimum cardinality of a binary code of length n and covering radius R. Four new linear codes found by computer search are also given. These include a [23,9]5 code, a [32,8]10 code, a [51,41]2 code, and a [45,20]8 code.

New constant weight codes are found by considering certain linear permutation groups. A code is obtained as a collection of orbits of words under such a group. This leads to a difficult optimization problem, where a stochastic search heuristic, tabu search, is used to find good solutions in a feasible amount of time. Nearly 40 new codes of length at most 28 are presented.

A matrix construction of nonlinear error-correcting codes is considered. It is shown how this construction and some related theorems can be applied to old codes to get new codes with minimum distance 3. In total 13 new binary single-error-correcting codes of length at most 511 are obtained.

A binary-error-correcting code of length 20 and minimum Hamming distance nine that has 42 codewords is constructed. This shows that A(20,9)>or=42.>