Let M be a random n = n -matrix over GF q such that for each entry M in i j w x ลฝ . M and for each nonzero field element โฃ the probability Pr M s โฃ is pr q y 1 , where i j ## ลฝ . p slog n y c rn and c is an arbitrary but fixed positive constant. The probability for a ลฝ . matrix entry to be zero
Rank properties of subspaces of symmetric and hermitian matrices over finite fields
โ Scribed by Jean-Guillaume Dumas; Rod Gow; John Sheekey
- Book ID
- 113623055
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 191 KB
- Volume
- 17
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let T be a skew-symmetric Toeplitz matrix with entries in a ยฎnite ยฎeld. For all positive integers n let n be the upper n ร n corner of T, with nullity m n m n . The sequence fm n X n P Ng satisยฎes a unimodality property and is eventually periodic if the entries of T satisfy a periodicity condition.
Some geometry of Hermitian matrices of order three over GF(q 2 ) is studied. The variety coming from rank 2 matrices is a cubic hypersurface M 3 7 of PG(8, q) whose singular points form a variety H corresponding to all rank 1 Hermitian matrices. Beside M 3 7 turns out to be the secant variety of H.