New Ternary and Quaternary Constant-Weight Equidistant Codes

Consider a finite set of q elements and containing a distinguished element ”zero”. The choice of a set does not matter in our context and we will use the set Zq of integers modulo q. Let Z q be the set of n-tuples (or vectors) over Zq and Z n,w q be the set of n-tuples over Zq of Hamming weight w. A code is called constant-weight if all the codewords have the same weight w. A code is called equidistant if all the distances between distinct codewords are d. Let Bq (n, d) denote the maximum number of codewords in an equidistant code over Zq of length n and distance d (called an (n,M, d)q equidistant code or EC) and Bq (n, d, w) denote the maximum number of codewords in an constantweight equidistant code over Zq of length n, distance d, and weight w (called an (n,M, d, w)q constant-weight equidistant code or ECWC). Code with parameters (n,Bq (n, d) , d)q is called optimal equidistant code. Code with parameters (n,Bq (n, d, w) , d, w)q is called optimal constant-weight equidistant code. Equidistant codes have been investigated by a large number of authors, mainly as examples of designs and other combinatorial objects [8]. Some works published on