Classification of binary/ternary one-error-correcting codes

Error-correcting codes with both binary and ternary coordinates are considered. The maximum cardinality of such a code with n(2) binary coordinates, n(3) ternary coordinates, and minimum distance d is denoted by N(n(2), n(3), d). A computer-aided method based on backtrack search and isomorph rejection is here used to settle many values of N(n(2), n(3), 3); several new upper bounds on this function are also obtained. For small parameters, a complete classification of optimal codes is carried out. It is shown that the maximum cardinality of a ternary one-error-correcting code of length 6 is 38 and that this code is unique. (C) 2000 Elsevier Science B.V. All rights reserved.