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Diskretnyi Analiz i Issledovanie Operatsii, 2023, Volume 30, Issue 2, Pages 5–14
DOI: https://doi.org/10.33048/daio.2023.30.753 (Mi da1319) 		 
A testing set for Preparata-like codes

A. Yu. Vasil'evaab

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov Street, 630090 Novosibirsk, Russia
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DOI: https://doi.org/10.33048/daio.2023.30.753
Abstract: The reconstruction of an object of a given class by its intersection with some (so-called testing) set is studied. For the class, we consider Preparata-like codes, i. e. nonlinear codes of length $n=2^{2m}-1,$ $m=2,3,\dots,$ with code distance $5$ and twice the size of a linear code of the same length and distance. We determine conditions under which the union of a few concentric spheres forms the testing set for Preparata-like codes.
Keywords: Hamming graph, Preparata code, perfect code, testing set, Krawtchouk polynomial.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF--2022--0017
This work was carried out within the framework of the state contract of the Sobolev Institute of Mathematics, project no. FWNF-2022-0017.
Received: 01.09.2022
Revised: 14.09.2022
Accepted: 16.09.2022
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 2, Pages 427–432
DOI: https://doi.org/10.1134/S1990478923020205
Document Type: Article
UDC: 519.8+518.25
Language: Russian
Citation: A. Yu. Vasil'eva, “A testing set for Preparata-like codes”, Diskretn. Anal. Issled. Oper., 30:2 (2023), 5–14; J. Appl. Industr. Math., 17:2 (2023), 427–432
Citation in format AMSBIB
\Bibitem{Vas23}
\by A.~Yu.~Vasil'eva
\paper A testing set for Preparata-like codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2023
\vol 30
\issue 2
\pages 5--14
\mathnet{http://mi.mathnet.ru/da1319}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 2
\pages 427--432
\crossref{https://doi.org/10.1134/S1990478923020205}
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