On two-weight codes

We consider q-ary (linear and nonlinear) block codes with exactly two distances: d and d+δ. We derive necessary conditions for existence of such codes (similar to the known conditions in the projective case). In the linear (but not necessary projective) case, we prove that under certain conditions t...

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Bibliographic Details
Published in:	Discrete mathematics Vol. 344; no. 5; p. 112318
Main Authors:	Boyvalenkov, P., Delchev, K., Zinoviev, D.V., Zinoviev, V.A.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-05-2021
Subjects:	Bounds for codes Linear programming bounds Linear two-weight codes Spherical codes Two-distance codes Two-weight codes Bounds for codes Two-weight codes Linear two-weight codes Spherical codes Two-distance codes Linear programming bounds
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Summary:	We consider q-ary (linear and nonlinear) block codes with exactly two distances: d and d+δ. We derive necessary conditions for existence of such codes (similar to the known conditions in the projective case). 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 greatest 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 qn<50 are presented.
ISSN:	0012-365X 1872-681X
DOI:	10.1016/j.disc.2021.112318