2020/05/27 by Boyvalenkov, P. G., Delchev, K. V., Zinoviev, D. V. +1
#94B05 #94B65 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2005.13623
We consider q-ary (linear and nonlinear) block codes with exactly two distances: d and d+δ. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) 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.