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
The minimum rank problem over the finite field of order 2: Minimum rank 3
โ Scribed by Wayne Barrett; Jason Grout; Raphael Loewy
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 590 KB
- Volume
- 430
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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For a simple graph G on n vertices, the minimum rank of G over a field F, written as mr F (G), is defined to be the smallest possible rank among all n ร n symmetric matrices over F whose (i, j)th entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A symmetric integ
It has been conjectured that over any non-prime finite field F p m and for any positive integer n, there exists a span n de Bruijn sequence over F p m which has the minimum possible linear complexity p nm&1 +n. We give a proof by construction that this conjecture is true.