On Binary/Ternary Error-Correcting Codes with Minimum Distance 4

Abstract

We consider error-correcting codes over mixed alphabets with n2 binary and n3 ternary coordinates, and denote the maximum cardinality of such a code with minimum distance d by N(n2, n3, d). We here study this function for short codes (n2+n3 ≤ 13) and d = 4. A computer-aided method is used to settle 14 values, and bounds for 34 other entries are improved. In the method used, codes are built up from smaller codes using backtracking and isomorphism rejection. Codes of short length are further classified.