This article is cited in 1 paper

Coding Theory

Improved upper bounds for the rate of separating and completely separating codes

I. V. Vorob'ev^a, V. S. Lebedev<sup>b

a</sup> Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia
^b Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: A binary code is said to be an $(s,\ell)$-separating code if for any two disjoint sets of its codewords of cardinalities at most s and respectively, there exists a coordinate in which all words of the first set have symbol $0$ while all words of the second have $1$. If, moreover, for any two sets there exists a second coordinate in which all words of the first set have $1$ and all words of the second have $0$, then such a code is called an $(s,\ell)$-completely separating code. We improve upper bounds on the rate of separating and completely separating codes.

Keywords: separating codes, completely separating codes, asymptotic rate, Plotkin bound.

UDC: 621.391 : 519.72

Received: 14.04.2022
Revised: 28.07.2022
Accepted: 30.07.2022

DOI: 10.31857/S0555292322030044

 English version: Problems of Information Transmission, 2022, 58:3, 242–253