Related papers: Weighted Generating Functions for Type II Lattices…
In this paper, we first generalize the class of linear codes by Ding and Ding (IEEE TIT, 61(11), pp. 5835-5842, 2015). Then we mainly study the augmented codes of this generalized class of linear codes. For one thing, we use Gaussian sums…
Delsarte showed that for any projective linear code over a finite field of characteristic p with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = (p^s)u and w2 = (p^s)(u+1). Moreover, he showed that…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new function spaces. Furthermore, the…
We present some applications of the Kudla-Millson and the Millson theta lift. The two lifts map weakly holomorphic modular functions to vector valued harmonic Maass forms of weight $3/2$ and $1/2$, respectively. We give finite algebraic…
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…
Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…
The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. They convey the structural information of a linear code and determine its performance in various applications, and have become one…
The main result of this paper is that an entire function $f$ that is in $L^2(\mathbb C^n,\psi)$ with respect to the weight $\psi(z)=2mH_S(z)+\gamma\log(1+|z|^2)$ is a polynomial with exponents in $m\widehat S_\Gamma$. Here $H_S$ is the…
We develop and analyze layer potential methods to represent harmonic functions on finitely-connected tori (i.e., doubly-periodic harmonic functions). The layer potentials are expressed in terms of a doubly-periodic and non-harmonic Green's…
The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. In this paper, we investigate the generalized Hamming weights of two classes of linear codes constructed from defining sets and determine them completely…
We discover an explicit expansion formula for the powers $s$ of the Euler Product (or Dedekind $\eta$-function) in terms of hook lengths of partitions, where the exponent $s$ is any complex number. Several classical formulas have been…
We study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l^p-boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated…
We obtain weight functions associated with $q$-linear and $q$-quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional for the Askey-Wilson polynomials and all the polynomial sequences in the…
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…
This paper investigates the relationship between the rank weight distribution of a linear code and that of its dual code. The main result of this paper is that, similar to the MacWilliams identity for the Hamming metric, the rank weight…
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through studying an algebro-geometric initial value problem.…
We study the connection between the theory of spherical designs and the question of extrema of the height function of lattices. More precisely, we show that a full-rank n-dimensional Euclidean lattice, all layers of which hold a spherical…
We show that the weight enumerator of any binary linear code is equal to the permanent of a 3-dimensional hypermatrix (3-matrix). We also show that each permanent is a determinant of a 3-matrix. As an application we write the dimer…
Combinatorial $t$-designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and $t$-designs has been…