260 research outputs found
Strongly regular graphs from weakly regular plateaued functions
The paper provides the first constructions of strongly regular graphs and
association schemes from weakly regular plateaued functions over finite fields
of odd characteristic. We generalize the construction method of strongly
regular graphs from weakly regular bent functions given by Chee et al. in
[Journal of Algebraic Combinatorics, 34(2), 251-266, 2011] to weakly regular
plateaued functions. In this framework, we construct strongly regular graphs
with three types of parameters from weakly regular plateaued functions with
some homogeneous conditions. We also construct a family of association schemes
of class p from weakly regular p-ary plateaued functions
A new class of three-weight linear codes from weakly regular plateaued functions
Linear codes with few weights have many applications in secret sharing
schemes, authentication codes, communication and strongly regular graphs. In
this paper, we consider linear codes with three weights in arbitrary
characteristic. To do this, we generalize the recent contribution of Mesnager
given in [Cryptography and Communications 9(1), 71-84, 2017]. We first present
a new class of binary linear codes with three weights from plateaued Boolean
functions and their weight distributions. We next introduce the notion of
(weakly) regular plateaued functions in odd characteristic and give
concrete examples of these functions. Moreover, we construct a new class of
three-weight linear -ary codes from weakly regular plateaued functions and
determine their weight distributions. We finally analyse the constructed linear
codes for secret sharing schemes.Comment: The Extended Abstract of this work was submitted to WCC-2017 (the
Tenth International Workshop on Coding and Cryptography
On a Class of Permutation Rational Functions Involving Trace Maps
Permutation rational functions over finite fields have attracted high
interest in recent years. However, only a few of them have been exhibited. This
article studies a class of permutation rational functions constructed using
trace maps on extensions of finite fields, especially for the cases of
quadratic and cubic extensions. Our achievements are obtained by investigating
absolute irreducibility of some polynomials in two indeterminates
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