42 research outputs found
Twin bent functions and Clifford algebras
This paper examines a pair of bent functions on and their
relationship to a necessary condition for the existence of an automorphism of
an edge-coloured graph whose colours are defined by the properties of a
canonical basis for the real representation of the Clifford algebra
Some other necessary conditions are also briefly examined.Comment: 11 pages. Preprint edited so that theorem numbers, etc. match those
in the published book chapter. Final post-submission paragraph added to
Section 6. in "Algebraic Design Theory and Hadamard Matrices: ADTHM,
Lethbridge, Alberta, Canada, July 2014", Charles J. Colbourn (editor), pp.
189-199, 201
Twin bent functions, strongly regular Cayley graphs, and Hurwitz-Radon theory
The real monomial representations of Clifford algebras give rise to two
sequences of bent functions. For each of these sequences, the corresponding
Cayley graphs are strongly regular graphs, and the corresponding sequences of
strongly regular graph parameters coincide. Even so, the corresponding graphs
in the two sequences are not isomorphic, except in the first 3 cases. The proof
of this non-isomorphism is a simple consequence of a theorem of Radon.Comment: 13 pages. Addressed one reviewer's questions in the Discussion
section, including more references. Resubmitted to JACODES Math, with updated
affiliation (I am now an Honorary Fellow of the University of Melbourne
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
Effective Construction of a Class of Bent Quadratic Boolean Functions
In this paper, we consider the characterization of the bentness of quadratic
Boolean functions of the form where ,
is even and . For a general , it is difficult to determine
the bentness of these functions. We present the bentness of quadratic Boolean
function for two cases: and , where and are two
distinct primes. Further, we give the enumeration of quadratic bent functions
for the case