ISSN:
1439-6912
Schlagwort(e):
06 C 10
;
15 A 06
;
11 T 99
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract LetA be a nonsingularn byn matrix over the finite fieldGF q ,k=⌊n/2⌋,q=p a ,a≥1, wherep is prime. LetP(A,q) denote the number of vectorsx in (GF q ) n such that bothx andAx have no zero component. We prove that forn≥2, and $$q 〉 2\left( {\begin{array}{*{20}c} {2n} \\ 3 \\ \end{array} } \right)$$ ,P(A,q)≥[(q−1)(q−3)] k (q−2) n−2k and describe all matricesA for which the equality holds. We also prove that the result conjectured in [1], namely thatP(A,q)≥1, is true for allq≥n+2≥3 orq≥n+1≥4.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01215347
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