an:05126004
Zbl 1110.11036
Clark, W. Edwin; Hou, Xiang-Dong; Mihailovs, Alec
The affinity of a permutation of a finite vector space
EN
Finite Fields Appl. 13, No. 1, 80-112 (2007).
00192013
2007
j
11T99 05A05 12E10
affinity; almost perfect nonlinear; finite field; vector space; affine subspace; permutation
Let \(f\) be a permutation of the \(n\)-dimensional vector space \(\mathbb F_q^n\) over a finite field \(\mathbb F_q\), then \(k\)-affinity(\(f\)) denotes the number of \(k\)-dimensional affine subspaces \(X\) of \(\mathbb F_q^n\) such that \(f(X)\) is again a \(k\)-dimensional affine subspace of \(\mathbb F_q^n\). The \(k\)-spectrum(\(n,q\)) is then the set of values \(k\)-affinity(\(f\)) for all permutations \(f\) of \(\mathbb F_q^n\). The authors show that, with few exceptions, \(0 \in k\)-spectrum(\(n,q\)) and present results on the largest values contained in \(k\)-spectrum(\(n,q\)). The paper is a continuation of \textit{X. D. Hou} [Discrete Appl. Math. 154, 313--325 (2006; Zbl 1089.94020)].
Wilfried Meidl (Istanbul)
Zbl 1089.94020