Line-parallelisms of PG$(n, 2)$ from Preparata-like codes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912556281495552 |
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| author | Heering, Philipp Taranchuk, Vladislav |
| author_facet | Heering, Philipp Taranchuk, Vladislav |
| contents | Partitions of the binary linear Hamming code into Preparata-like codes are known to induce line-parallelisms of PG$(n, 2)$. In this paper, we show that if $P$ is any Preparata-like code contained in the binary linear Hamming code $H$ of the same length, then $H$ can be partitioned into additive translates of $P$. This generalizes a result of Baker, van Lint, and Wilson who prove this fact for the class of generalized Preparata codes. We give an explicit description for line-parallelisms obtained from such a partition via crooked Preparata-like codes and establish an equivalence criterion for such line-parallelisms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_19901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Line-parallelisms of PG$(n, 2)$ from Preparata-like codes Heering, Philipp Taranchuk, Vladislav Combinatorics 51E23, 11T06, 94A60 Partitions of the binary linear Hamming code into Preparata-like codes are known to induce line-parallelisms of PG$(n, 2)$. In this paper, we show that if $P$ is any Preparata-like code contained in the binary linear Hamming code $H$ of the same length, then $H$ can be partitioned into additive translates of $P$. This generalizes a result of Baker, van Lint, and Wilson who prove this fact for the class of generalized Preparata codes. We give an explicit description for line-parallelisms obtained from such a partition via crooked Preparata-like codes and establish an equivalence criterion for such line-parallelisms. |
| title | Line-parallelisms of PG$(n, 2)$ from Preparata-like codes |
| topic | Combinatorics 51E23, 11T06, 94A60 |
| url | https://arxiv.org/abs/2508.19901 |