Crooked binomials

被引：20

作者：

Bierbrauer, Juergen ^{[1
]}

Kyureghyan, Gohar M. ^{[2
]}

机构：

[1] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[2] Otto Von Guericke Univ, Dept Math, Magdeburg, Germany

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2008年 / 46卷 / 03期

关键词：

crooked functions; APN functions; codes; cyclotomic cosets; preparata codes;

D O I：

10.1007/s10623-007-9157-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A function f : GF(2(r)) -> GF(2(r)) is called crooked if the sets {f(x) + f(x + a)vertical bar x is an element of GF(2(r))} is an affine hyperplane for any nonzero a epsilon GF(2(r)). We prove that a crooked binomial function f(x) = x(d)+ ux(e) defined on GF(2(r)) satisfies that both exponents d, e have 2-weights at most 2.

引用

页码：269 / 301

页数：33

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