Maximal partial line spreads of non-singular quadrics

For n >= 9 , we construct maximal partial line spreads for non-singular quadrics of for every size between approximately and , for some small constants and . These results are similar to spectrum results on maximal partial line spreads in finite projective spaces by Heden, and by Gacs and SzAnyi. These results also extend spectrum results on maximal partial line spreads in the finite generalized quadrangles and by Pepe, Roing and Storme

Unextendible mutually unbiased bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)

We consider questions posed in a recent paper of Mandayam et al. (2014) on the nature of unextendible mutually unbiased bases. We describe a conceptual framework to study these questions, using a connection proved by the author in Thas (2009) between the set of nonidentity generalized Pauli operators on the Hilbert space of N d-level quantum systems, d a prime, and the geometry of non-degenerate alternating bilinear forms of rank N over finite fields F d We then supply alternative and short proofs of results obtained in Mandayam et al. (2014), as well as new general bounds for the problems considered in loc. cit. In this setting, we also solve Conjecture 1 of Mandayam et al. (2014) and speculate on variations of this conjecture

The maximum size of a partial spread in H(5, q²) is q³+1

AbstractIn this paper, we show that the largest maximal partial spreads of the hermitian variety H(5,q2) consist of q3+1 generators. Previously, it was only known that q4 is an upper bound for the size of these partial spreads. We also show for q⩾7 that every maximal partial spread of H(5,q2) contains at least 2q+3 planes. Previously, only the lower bound q+1 was known

Johnson type bounds for mixed dimension subspace codes

Subspace codes, i.e., sets of subspaces of $\mathbb{F}_q^v$, are applied in random linear network coding. Here we give improved upper bounds for their cardinalities based on the Johnson bound for constant dimension codes.Comment: 16 pages, typos correcte

A geometric proof of the upper bound on the size of partial spreads in H(4n+1, q²)

We give a geometric proof of the upper bound of q(2n+1) + 1 on the size of partial spreads in the polar space H(4n + 1, q(2)). This bound is tight and has already been proved in an algebraic way. Our alternative proof also yields a characterization of the partial spreads of maximum size in H(4n + 1, q(2))