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Probl. Peredachi Inf., 2016, Volume 52, Issue 2, Pages 46–60 (Mi ppi2203)  

Coding Theory

Almost cover-free codes

N. A. Polyanskyab

a Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
b Probability Theory Department, Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We say that an $s$-subset of codewords of a code $X$ is ($(s,\ell)$-bad if $X$ contains $\ell$ other codewords such that the conjunction of these $\ell$ words is covered by the disjunction of the words of the $s$-subset. Otherwise, an $s$-subset of codewords of $X$ is said to be $(s,\ell)$-bad. A binary code $X$ is called a disjunctive $(s,\ell)$ cover-free (CF) code if $X$ does not contain $(s,\ell)$-bad subsets. We consider a probabilistic generalization of $(s,\ell)$ CF codes: we say that a binary code is an $(s,\ell)$ almost cover-free (ACF) code if almost all $s$-subsets of its codewords are $(s,\ell)$-good. The most interesting result is the proof of a lower and an upper bound for the capacity of $(s,\ell)$ ACF codes; the ratio of these bounds tends as $s\to\infty$ to the limit value $\log_2e/(\ell e)$.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.


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English version:
Problems of Information Transmission, 2016, 52:2, 142–155

Bibliographic databases:

UDC: 621.391.15
Received: 11.06.2015
Revised: 23.11.2015

Citation: N. A. Polyansky, “Almost cover-free codes”, Probl. Peredachi Inf., 52:2 (2016), 46–60; Problems Inform. Transmission, 52:2 (2016), 142–155

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