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Problemy Peredachi Informatsii, 2022, Volume 58, Issue 4, Pages 62–83
DOI: https://doi.org/10.31857/S0555292322040064 (Mi ppi2384) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Coding Theory

On codes with distances $d$ and $n$

P. Boyvalenkova, K. Delcheva, V. A. Zinovievb, D. V. Zinovievb

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
Full-text PDF (313 kB) First page Citations (3)
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DOI: https://doi.org/10.31857/S0555292322040064
Abstract: We enumerate all $q$-ary additive (in particular, linear) block codes of length $n$ and cardinality $N\geqslant q^2$ with exactly two distances: $d$ and $n$. For arbitrary codes of length $n$ with distances $d$ and $n$, we obtain upper bounds on the cardinality via linear programming and using relationships to $2$-distance sets on a Euclidean sphere.
Keywords: two-distance code, two-weight code, linear two-weight code, difference matrix, maximal arc, Latin square, orthogonal array, bounds for codes, linear programming bounds, spherical code.
Funding agency Grant number
Bulgarian National Science Fund KP-06-Russia/33-2020
KP-06-N32/2-2019
Russian Foundation for Basic Research 20-51-18002
The research of P. Boyvalenkov was supported in part by the Bulgarian National Science Foundation, project no. KP-06-Russia/33-2020.
The research of K. Delchev was supported in part by the Bulgarian National Science Foundation, project no. KP-06-N32/2-2019.
The research of V.A. Zinoviev and D.V. Zinoviev was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences within the program of fundamental research on the topic “Mathematical Foundations of the Theory of Error-Correcting Codes” and was also supported by the National Science Foundation of Bulgaria under project no. 20-51-18002.
Received: 14.11.2022
Revised: 25.11.2022
Accepted: 28.11.2022
English version:
Problems of Information Transmission, 2022, Volume 58, Issue 4, Pages 352–371
DOI: https://doi.org/10.1134/S0032946022040068
Bibliographic databases:
Document Type: Article
UDC: 621.391 : 519.725
Language: Russian
Citation: P. Boyvalenkov, K. Delchev, V. A. Zinoviev, D. V. Zinoviev, “On codes with distances $d$ and $n$”, Probl. Peredachi Inf., 58:4 (2022), 62–83; Problems Inform. Transmission, 58:4 (2022), 352–371
Citation in format AMSBIB
\Bibitem{BoyDelZin22}
\by P.~Boyvalenkov, K.~Delchev, V.~A.~Zinoviev, D.~V.~Zinoviev
\paper On codes with distances $d$ and $n$
\jour Probl. Peredachi Inf.
\yr 2022
\vol 58
\issue 4
\pages 62--83
\mathnet{http://mi.mathnet.ru/ppi2384}
\crossref{https://doi.org/10.31857/S0555292322040064}
\edn{https://elibrary.ru/NAWXWG}
\transl
\jour Problems Inform. Transmission
\yr 2022
\vol 58
\issue 4
\pages 352--371
\crossref{https://doi.org/10.1134/S0032946022040068}
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