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On the Ranks of Skew Centrosymmetric Matrices over Finite Fields

✍ Scribed by William C. Waterhouse

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
169 KB
Volume
4
Category
Article
ISSN
1071-5797

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Let M be a random n = n -matrix over GF q such that for each entry M in i j w x Ž . M and for each nonzero field element ␣ the probability Pr M s ␣ is pr q y 1 , where i j ## Ž . p slog n y c rn and c is an arbitrary but fixed positive constant. The probability for a Ž . matrix entry to be zero

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Let V be a vector space of dimension n β‰₯ 3 over GF(2). We are concerned with the incidence of k-dimensional subspaces in (k + 2)-dimensional subspaces where 1 ≀ k ≀ n -2. We compute here an upper bound for the rank of the associated incidence matrices over GF(2).