ON THE NUMBER OF NOWHERE ZERO POINTS IN LINEAR MAPPINGS

被引：5

作者：

BAKER, RD

BONIN, J

LAZEBNIK, F

SHUSTIN, E

机构：

[1] UNIV DELAWARE,DEPT MATH SCI,NEWARK,DE 19716

[2] TEL AVIV UNIV,SCH MATH SCI,IL-69978 TEL AVIV,ISRAEL

[3] GEORGE WASHINGTON UNIV,DEPT MATH,WASHINGTON,DC 20052

来源：

COMBINATORICA | 1994年 / 14卷 / 02期

关键词：

AMS subject classification code (1991): 06C10; 15A06; 11T99;

D O I：

10.1007/BF01215347

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a nonsingular n by n matrix over the finite field GF(q), k = right perpendicularn/2left perpendicular, q = p(a), a greater-than-or-equal-to 1, where p is prime. Let P(A,q) denote the number of vectors x in (GF(q))n such that both x and Ax have no zero component. We prove that for n greater-than-or-equal-to 2, and q > 2 (2n3), P(A,q) greater-than-or-equal-to [(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) greater-than-or-equal-to 1, is true for all q greater-than-or-equal-to n + 2 greater-than-or-equal-to 3 or q greater-than-or-equal-to n + 1 greater-than-or-equal-to 4.

引用

页码：149 / 157

页数：9