Classification of binary/ternary one-error-correcting codes

摘要

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.