Abstract:We study two-distance sets in standard $d$-dimensional quadratic spaces over finite fields. In characteristic $3$, we construct sets attaining the full Larman--Rogers--Seidel bound, showing that Blokhuis' Euclidean bound $\binom{d+2}{2}$ need not hold over finite fields. We prove a rank-sensitive replacement which precisely measures the failure of positive definiteness. We also show that the Blokhuis bound $\binom{d+2}{2}$ is attained over a suitable finite field exactly for each $d\neq6$; in the exceptional dimension $d=6$, the exact maximum is $27$.
From: Jozsef Solymosi [view email]
[v1]
Wed, 31 Dec 2025 03:27:17 UTC (11 KB)
[v2]
Mon, 27 Jul 2026 15:07:03 UTC (19 KB)
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