955 research outputs found
On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees
In the literature, few constructions of -variable rotation symmetric bent
functions have been presented, which either have restriction on or have
algebraic degree no more than . In this paper, for any even integer
, a first systemic construction of -variable rotation symmetric
bent functions, with any possible algebraic degrees ranging from to , is
proposed
Semi-regular Relative Difference Sets with Large Forbidden Subgroups
Motivated by a connection between semi-regular relative difference sets and
mutually unbiased bases, we study relative difference sets with parameters
in groups of non-prime-power orders. Let be an odd prime. We
prove that there does not exist a relative difference set in any
group of order , and an abelian relative difference set can
only exist in the group . On the other hand, we
construct a family of non-abelian relative difference sets with parameters
, where is an odd prime power greater than 9 and
(mod 4). When is a prime, , and 1 (mod 4), the
non-abelian relative difference sets constructed here are
genuinely non-abelian in the sense that there does not exist an abelian
relative difference set with the same parameters
Class of Quadratic Almost Bent Functions That Is EA-Inequivalent to Permutations
The permutation relationship for the almost bent (AB) functions in the finite field is a significant issue. Li and Wang proved that a class of AB functions with algebraic degree 3 is extended affine- (EA-) inequivalent to any permutation. This study proves that another class of AB functions, which was developed in 2009, is EA-inequivalent to any permutation. This particular AB function is the first known quadratic class EA-inequivalent to permutation
On upper bounds for algebraic degrees of APN functions
We study the problem of existence of APN functions of algebraic degree over \ftwon. We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which mean, in particular, that for most of the known APN functions over \ftwon the function is not APN, and changing a value of in a single point results in non-APN functions
Self-embeddings of Hamming Steiner triple systems of small order and APN permutations
The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n = 2 m − 1 for small m (m ≤ 22), is given. As far as we know, for m ∈ {5, 7, 11, 13, 17, 19}, all given self-embeddings in closed surfaces are new. Moreover, they are cyclic for all m and nonorientable at least for all m ≤ 19. For any non prime m, the nonexistence of such self-embeddings in a closed surface is proven. The rotation line spectrum for self-embeddings of Hamming Steiner triple systems in pseudosurfaces with pinch points as an invariant to distinguish APN permutations or, in general, to classify permutations, is also proposed. This invariant applied to APN monomial power permutations gives a classification which coincides with the classification of such permutations via CCZ-equivalence, at least up to m ≤ 17
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