О ядрах нелинейных квазисовершенных кодов Full article
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Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2026, Volume: 23, Number: 1, Pages: 137–148 Pages count : 12 DOI: 10.33048/semi.2026.23.010 | ||
| Tags | perfect code, quasi-perfect code, nonlinear code, generalized Reed–Muller code, code rank, code kernel, Galois geometry. | ||
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0011 |
Abstract:
We consider quasi-perfect codes with packing radius 1 over a finite field of q elements. We call these codes 1-quasiperfect q-ary codes.We study the structural properties of nonlinear 1-quasi-perfect q-ary codes, namely the rank and dimension of the kernel. In this paper, we propose a construction of 1-quasi-perfect q-ary codes with parameters of generalized Reed-Muller codes of order r = (q − 1)m − 2, where m is a positive integer. For q ≥ 3, m ≥ 2, the proposed construction allows one to construct nonlinear 1-quasi-perfect q-ary codes with different kernel dimensions. The dimensions of the kernel of nonlinear 1-quasi-perfect q-ary codes constructed using the proposed construction are calculated.
Cite:
Романов А.М.
О ядрах нелинейных квазисовершенных кодов
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2026. Т.23. №1. С.137–148. DOI: 10.33048/semi.2026.23.010
О ядрах нелинейных квазисовершенных кодов
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2026. Т.23. №1. С.137–148. DOI: 10.33048/semi.2026.23.010
Dates:
| Submitted: | Jul 31, 2025 |
| Accepted: | Feb 6, 2026 |
| Published online: | Mar 19, 2026 |
Identifiers:
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