J. Borges, V. A. Zinoviev, D. V. Zinoviev, “On the classification of completely regular codes with covering radius two and antipodal duals”, Probl. Peredachi Inf., 2023, Volume 59, Issue 3,Pages <nobr>26

Coding Theory

On the classification of completely regular codes with covering radius two and antipodal duals

J. Borges^a, V. A. Zinoviev^b, D. V. Zinoviev^b

^a Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Barcelona, Spain
^b Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia

Abstract: We classify all linear completely regular codes which have covering radius $\rho=2$ and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights $d$ and $n$.

Keywords: linear completely regular code, code with covering radius $2$, code with an antipodal dual, two-weight code, difference matrix, Latin square, projective oval, equidistant code, Hadamard matrix, Hamming code, maximal arc.

UDC: 621.391 : 519.725

Received: 14.06.2023
Revised: 27.11.2023
Accepted: 27.11.2023

DOI: 10.31857/S0555292323030026