BOUNDS FOR BINARY-CODES THAT ARE MULTIPLE COVERINGS OF THE FARTHEST-OFF POINTS

A binary code C subset of or equal to F-2(n) with M codewords is calle d an (n, M, r, mu) multiple covering of the farthest-off points (MCF) if the Hamming spheres of radius r centered at the codewords cover the whole space F-2(n) and every x is an element of F-2(n) such that d(x, C) = r is covered by at least mu codewords. The minimum possible cardi nality F(n, r, mu) of such a code is studied and tables of upper bound s on F(n, r, mu) for n less than or equal to 16,r less than or equal t o 4,mu less than or equal to 4 are given.