Geodesic
Constant rank-distance sets of Hermitian matrices and partial spreads in Hermitian polar spaces
Rod Gow1 ; Michel Lavrauw2 ; John Sheekey2 ; Frédéric Vanhove3
1University College Dublin
2Università di Padova
3Ghent Universtity
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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In this paper we investigate partial spreads of $H(2n-1,q^2)$ 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 $H(2n-1,q^2)$. We prove upper bounds for constant rank-distance sets for even rank, construct large examples of these, and construct maximal partial spreads of $H(3,q^2)$ for a range of sizes.
DOI : 10.37236/3534
Classification : 05B25, 51E23, 51A50, 15A03
Mots-clés : partial spread, Hermitian variety, Hermitian matrix, rank-distance

Rod Gow  1   ; Michel Lavrauw  2   ; John Sheekey  2   ; Frédéric Vanhove  3

1 University College Dublin
2 Università di Padova
3 Ghent Universtity 
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     author = {Rod Gow and Michel Lavrauw and John Sheekey and Fr\'ed\'eric Vanhove},
     title = {Constant rank-distance sets of {Hermitian} matrices and partial spreads in {Hermitian} polar spaces},
     journal = {The electronic journal of combinatorics},
     year = {2014},
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     number = {1},
     doi = {10.37236/3534},
     zbl = {1300.05050},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3534/}
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Rod Gow; Michel Lavrauw; John Sheekey; Frédéric Vanhove. Constant rank-distance sets of Hermitian matrices and partial spreads in Hermitian polar spaces. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3534

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