RU
Bounds on the parameters of Tanner codes on the graph of projective space
Received: 29 Apr 2026 Revised: 05 May 2026 Accepted: 08 May 2026
Published: 2026, vol. 30, issue 3, pp. 189–216
Abstract
This paper considers Tanner codes constructed on the incidence graph of points and hyperplanes of a projective space, with projective Reed–Muller codes as component codes. The assignment of symbols of local codes to edges is performed so that the resulting Tanner code inherits the symmetry of the projective space. Lower bounds on the minimum distance and dimension of such codes are obtained. In particular, it is shown that, for certain parameter values, these codes are asymptotically good.
Keywords: Tanner codes, incidence graph, projective space, minimum distance, code dimension.
BibTeX
@article{IS-Yusufova-Kalachev2026,
author = {Yusufova, Alina Almasovna and Kalachev, Gleb Vyacheslavovich},
title = {{Bounds on the parameters of Tanner codes on the graph of projective space}},
journal = {Intelligent Systems. Theory and Applications},
year = {2026},
volume = {30},
number = {3},
pages = {189--216},
}
AMSBIB
\Bibitem{IS-Yusufova-Kalachev2026}
\by A.\,A.~Yusufova, G.\,V.~Kalachev
\paper Bounds on the parameters of Tanner codes on the graph of projective space
\jour Intelligent Systems. Theory and Applications
\yr 2026
\vol 30
\issue 3
\pages 189--216
\lang In Russian