The maximum size of a partial spread in a finite projective space

2016/05/16 by Nastase, Esmeralda, Sissokho, Papa · 2 citations
#05B25 #51E23 #94B25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.04824

Abstract

Let n and t be positive integers with t(q^r-1)/(q-1), then the maximum size, i.e., cardinality, of a partial (t-1)-spread of \rm PG(n-1,q) is (qⁿ-q^t+r)/(q^t-1)+1. This essentially settles a main open problem in this area. Prior to this result, this maximum size was only known for r∈\0,1\ and for r=q=2.

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• Generalized Hamming weights of additive codes and geometric counterparts
• Upper bounds on the length of quasi-MDS codes

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