Good equidistant codes constructed from certain combinatorial designs

An (n,M,d;q)(n,M,d;q) code is called equidistant code if the Hamming distance between any two codewords is d  . It was proved that for any equidistant (n,M,d;q)(n,M,d;q) code, d⩽nM(q-1)/(M-1)qd⩽nM(q-1)/(M-1)q(=dopt=dopt, say). A necessary condition for the existence of an optimal equidistant code is that doptdopt be an integer. If doptdopt is not an integer, i.e. the equidistant code is not optimal, then the code with d=⌊dopt⌋d=⌊dopt⌋ is called good equidistant code, which is obviously the best possible one among equidistant codes with parameters n,Mn,M and q. In this paper, some constructions of good equidistant codes from balanced arrays and nested BIB designs are described.