On two-weight codes

P. G. Boyvalenkov; K. V. Delchev; D. V. Zinoviev; V. A. Zinoviev

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arXiv · 2005.13623

On two-weight codes

P. G. Boyvalenkov·K. V. Delchev·D. V. Zinoviev·V. A. Zinoviev

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Abstract

We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+\delta$. 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 $\delta > 1$ implies the following equality of great common divisors: $(d,q) = (\delta,q)$. 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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P. G. Boyvalenkov, K. V. Delchev, D. V. Zinoviev, V. A. Zinoviev. 2020-05-27. On two-weight codes. https://arxiv.org/abs/2005.13623

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