相关论文: A new family of semifields with 2 parameters
We construct and describe the basic properties of a family of semifields in characteristic $2.$ The construction relies on the properties of projective polynomials over finite fields. We start by associating non-associative products to each…
We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both…
In this paper, two new classes of perfect nonlinear functions over $\mathbb{F}_{p^{2m}}$ are proposed, where $p$ is an odd prime. Furthermore, we investigate the nucleus of the corresponding semifields of these functions and show that the…
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…
Recently, the interest in semifields has increased due to the discovery of several new families and progress in the classification problem. Commutative semifields play an important role since they are equivalent to certain planar functions…
We define two-parameter families of noncommutative symmetric functions and quasi-symmetric functions, which appear to be the proper analogues of the Macdonald symmetric functions in these settings.
We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very…
We find a five-parameter family of partial differential systems in two variables with two polynomial Hamiltonians. We give its symmetry and holomorphy conditions. These symmetries, holomorphy conditions and invariant divisors are new.
We consider in this paper the semiparametric mixture of two distributions equal up to a shift parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. In…
It is proved that the numerical semigroups associated to the combinatorial configurations satisfy a family of non-linear symmetric patterns. Also, these numerical semigroups are studied for two particular classes of combinatorial…
We present two infinite families of APN functions where the degree of the field is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which…
We investigate the connections between various noncommutative analogues of Hall-Littlewood and Macdonald polynomials, and define some new families of noncommutative symmetric functions depending on two sequences of parameters.
We classify the rank two commutative semifields which are 8-dimensional over their center $\mathbb{F}_{q}$. This is done using computational methods utilizing the connection to linear sets in $\mathrm{PG}(2,q^{4})$. We then apply our…
The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We…
In this work, we present two new families of quadratic APN functions. The first one (F1) is constructed via biprojective polynomials. This family includes one of the two APN families introduced by G\"olo\v{g}lu in 2022. Then, following a…
In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function…
We introduce a new family of non-negative real-valued functions on a $C^*$-algebra $\mathcal{A}$, i.e., for $0\leq \mu \leq 1,$ $$\|a\|_{\sigma_{\mu}}= \text{sup}\left\lbrace \sqrt{|f(a)|^2 \sigma_{\mu} f(a^*a)}: f\in \mathcal{A}', \,…
The q-Legendre polynomials can be treated as some special "functions in the quantum double cosets $U(1)\setminus SU_q(2)/U(1)$". They form a family (depending on a parameter $q$) of polynomials in one variable. We get their further…
It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the…
In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…