Constant rank-distance sets of hermitian matrices and partial spreads in hermitian polar spaces

2012/08/09 by Rod Gow, Gow, Rod, Michel Lavrauw +5
Computer Science · Mathematics · #05B25 #15A03 #51A50 #51E23 #Advanced Algebra and Geometry #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO #msc:05B25 #msc:15A03 #msc:51A50 #msc:51E23

paper · pdf · doi:10.48550/arxiv.1208.1903

openalex publication_date 2012/08/09 · arxiv created 2013/06/04 · arxiv updated 2013/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate partial spreads of H(2n-1,q²) through the related notion of partial spread sets of hermitian matrices, and the more general notion of constant rank-distance sets. We prove a tight upper bound on the maximum size of a linear constant rank-distance set of hermitian matrices over finite fields, and as a consequence prove the maximality of extensions of symplectic semifield spreads as partial spreads of H(2n-1,q²). We prove upper bounds for constant rank-distance sets for even rank, construct large examples of these, and construct maximal partial spreads of H(3,q²) for a range of sizes.

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