TY - JOUR
T1 - On the number of nowhere zero points in linear mappings
AU - Baker, R. D.
AU - Bonin, J.
AU - Lazebnik, F.
AU - Shustin, E.
PY - 1994/6
Y1 - 1994/6
N2 - Let A be a nonsingular n by n matrix over the finite field GFq, k=⌊n/2⌋, q=pa, a≥1, where p is prime. Let P(A,q) denote the number of vectors x in (GFq)n such that both x and Ax have no zero component. We prove that for n≥2, and {Mathematical expression}, P(A,q)≥[(q-1)(q-3)]k(q-2)n-2k and describe all matrices A for which the equality holds. We also prove that the result conjectured in [1], namely that P(A,q)≥1, is true for all q≥n+2≥3 or q≥n+1≥4.
AB - Let A be a nonsingular n by n matrix over the finite field GFq, k=⌊n/2⌋, q=pa, a≥1, where p is prime. Let P(A,q) denote the number of vectors x in (GFq)n such that both x and Ax have no zero component. We prove that for n≥2, and {Mathematical expression}, P(A,q)≥[(q-1)(q-3)]k(q-2)n-2k and describe all matrices A for which the equality holds. We also prove that the result conjectured in [1], namely that P(A,q)≥1, is true for all q≥n+2≥3 or q≥n+1≥4.
KW - AMS subject classification code (1991): 06C10, 15A06, 11T99
UR - http://www.scopus.com/inward/record.url?scp=0008990495&partnerID=8YFLogxK
U2 - 10.1007/BF01215347
DO - 10.1007/BF01215347
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0008990495
SN - 0209-9683
VL - 14
SP - 149
EP - 157
JO - Combinatorica
JF - Combinatorica
IS - 2
ER -