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arXiv · 2508.19901

Line-parallelisms of PG$(n, 2)$ from Preparata-like codes

Philipp Heering·Vladislav Taranchuk
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Abstract

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.

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Philipp Heering, Vladislav Taranchuk. 2025-08-27. Line-parallelisms of PG$(n, 2)$ from Preparata-like codes. https://arxiv.org/abs/2508.19901

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