On q-ary codes with two distances d and d+1
P. Boyvalenkov, K. Delchev, D. Zinoviev, V. Zinoviev
TL;DR
This paper investigates q-ary block codes with exactly two distances, providing constructions, bounds on their size, and tables for small parameters, extending understanding of their structure and limitations.
Contribution
It introduces new constructions and bounds for q-ary codes with two distances, generalizing linear equidistant code modifications and offering comprehensive bounds for small cases.
Findings
Constructed several q-ary codes with two distances d and d+1.
Derived upper bounds for the maximum size of such codes.
Presented tables of bounds for small q and n.
Abstract
The -ary block codes with two distances and are considered. Several constructions of such codes are given, as in the linear case all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for the maximum cardinality of such codes is derived. Tables of lower and upper bounds for small and are presented.
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Taxonomy
Topicsgraph theory and CDMA systems · Mathematical Approximation and Integration · Coding theory and cryptography