On Nonlinear 1-Quasi-perfect Codes and Their Structural Properties

On Nonlinear 1-Quasi-perfect Codes and Their Structural Properties Full article

Journal

Problems of Information Transmission
ISSN: 0032-9460 , E-ISSN: 1608-3253

Output data

Year: 2024, Volume: 60, Number: 3, Pages: 141–154 Pages count : 13 DOI: 10.1134/S0032946024030013

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0017

We consider nonlinear quasi-perfect codes with packing radius 1 over a finite field of q elements. We call these codes nonlinear 1-quasi-perfect q-ary codes. We study the structural properties of nonlinear 1-quasi-perfect q-ary codes, namely the rank and the dimension of the kernel. We prove that for n = qm and any t ∈ {1, 2, . . . ,m + 1} there exist nonlinear 1-quasi- perfect q-ary codes of length n and rank n−m−1+t. Here, m ≥ 5 for q = 3 and 4, m ≥ 4 for 5 ≤ q ≤ 19, and m ≥ 3 for q ≥ 23. In particular, we prove that there exist full-rank nonlinear 1-quasi-perfect q-ary codes. Also, for some nonlinear 1-quasi-perfect q-ary codes we calculate the kernel dimension.

Romanov A.M.
On Nonlinear 1-Quasi-perfect Codes and Their Structural Properties
Problems of Information Transmission. 2024. V.60. N3. P.141–154. DOI: 10.1134/S0032946024030013 WOS Scopus РИНЦ OpenAlex

Романов А.М.
О ранге нелинейных квазисовершенных кодов над конечными полями
Проблемы передачи информации. 2024. Т.60. №3. С.3-12. DOI: 10.31857/S055529232403001X РИНЦ OpenAlex

Submitted:	Jun 3, 2024
Accepted:	Nov 16, 2024
Published print:	Jan 5, 2025
Published online:	Jan 5, 2025

Web of science:	WOS:001390723600002
Scopus:	2-s2.0-85214351030
Elibrary:	79026348
OpenAlex:	W4406073962

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