On two-weight codes
| Autor: | Boyvalenkov, P. G., Delchev, K. V., Zinoviev, D. V., Zinoviev, V. A. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: submitted |
| Databáze: | arXiv |
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