On two-weight codes
We consider q-ary block codes with exactly two distances: d and d+δ. Several combinatorial constructions of optimal such codes are given. In the linear case, we prove that under certain conditions the existence of such linear 2-weight code with δ > 1 implies the following equality of great common divisors: (d,q) = (δ,q). Upper bounds for the maximum cardinality of such codes are derived by linear programming and from few-distance spherical codes. Tables of lower and upper bounds for small q = 2,3,4 and q n < 50 are presented.
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