Projective tilings and full-rank perfect codes Full article
| Journal |
Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586 |
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| Output data | Year: 2023, Volume: 91, Number: 10, Pages: 3293–3303 Pages count : 11 DOI: 10.1007/s10623-023-01256-y | ||
| Tags | perfect codes, tilings, group factorization, full-rank tilings, projective geometry | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-11-00266 |
Abstract:
A tiling of a vector space S is the pair (U, V ) of its subsets such that every vector in S is uniquely represented as the sum of a vector from U and a vector from V . A tiling is connected to a perfect codes if one of the sets, say U, is projective, i.e., the union of one-dimensional subspaces of S. A tiling (U, V ) is full-rank if the affine span of each of U, V is S. For finite non-binary vector spaces of dimension at least 6 (at least 10), we construct full-rank tilings (U, V ) with projective U (both U and V , respectively). In particular, that construction gives a full-rank ternary 1-perfect code of length 13, solving a known problem. We also discuss the treatment of tilings with projective components as factorizations of projective spaces.
Cite:
Krotov D.S.
Projective tilings and full-rank perfect codes
Designs, Codes and Cryptography. 2023. V.91. N10. P.3293–3303. DOI: 10.1007/s10623-023-01256-y WOS Scopus OpenAlex
Projective tilings and full-rank perfect codes
Designs, Codes and Cryptography. 2023. V.91. N10. P.3293–3303. DOI: 10.1007/s10623-023-01256-y WOS Scopus OpenAlex
Dates:
| Submitted: | Jul 11, 2022 |
| Accepted: | May 27, 2023 |
| Published print: | Jun 13, 2023 |
| Published online: | Jun 13, 2023 |
Identifiers:
| Web of science: | WOS:001005819600001 |
| Scopus: | 2-s2.0-85163094966 |
| OpenAlex: | W4380090997 |
Citing:
| DB | Citing |
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| OpenAlex | 1 |