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On inequivalent representations of matroids over non-prime fields

✍ Scribed by Jim Geelen; Bert Gerards; Geoff Whittle

Book ID
108167489
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
117 KB
Volume
100
Category
Article
ISSN
0095-8956

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Kahn conjectured in 1988 that, for each prime power q, there is an integer n(q) such that no 3-connected GF(q)-representable matroid has more than n(q) inequivalent GF(q)-representations. At the time, this conjecture was known to be true for q=2 and q=3, and Kahn had just proved it for q=4. In this

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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.