相关论文: Duursma's reduced polynomial

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…

The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of…

Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of $q$-ary linear codes derived from irreducible cyclic…

Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…

In a paper from 2010, Budarina, Dickinson and Levesley studied the rational approximation properties of curves parametrized by polynomials with integral coefficients in Euclidean space of arbitrary dimension. Assuming the dimension is at…

We consider linear codes over some fixed finite field extension over an arbitrary finite field. Gabidulin introduced rank metric codes, by endowing linear codes over the extension field with a rank weight over the base field and studied…

The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials. For…

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields…

We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of…

We introduce and study the minimum distance function of a graded ideal in a polynomial ring with coefficients in a field, and show that it generalizes the minimum distance of projective Reed-Muller-type codes over finite fields. This gives…

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of $t$-weight linear codes over ${\mathbb F}_{q}$ are presented with…

Let $q$ be an odd prime power and let $X(m,q)$ be the set of symmetric bilinear forms on an $m$-dimensional vector space over $\mathbb{F}_q$. The partition of $X(m,q)$ induced by the action of the general linear group gives rise to a…

q-ary cumulative-separable $\Gamma(L,G^{(j)})$-codes $L=\{ \alpha \in GF(q^{m}):G(\alpha )\neq 0 \}$ and $G^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q$ are considered. The relation between different codes from this class is demonstrated. Improved…

We explicitly determine the values of reduced cyclotomic periods of order $2^m$, $m\ge 4$, for finite fields of characteristic $p\equiv 3$ or $5\pmod{8}$. These evaluations are applied to obtain explicit factorizations of the corresponding…

We show that Seiberg-like duality of $\mathcal{N}=1$ gauge theory coupled with tensor chiral fields and fundamental chiral fields works if the meson spectrum built from the tensor fields takes particular form: a) It should be truncated; b)…

We generalize the concept of reduced Arakelov divisors and define $C$-reduced divisors for a given number $C \geq 1$. These $C$-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper,…

Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions,…

Using commutative algebra methods we study the generalized minimum distance function (gmd function) and the corresponding generalized footprint function of a graded ideal in a polynomial ring over a field. The number of solutions that a…

Given a squarefree monomial ideal $I$ of a polynomial ring $Q$, we show that if the minimal free resolution $\mathbb{F}$ of $Q/I$ admits the structure of a differential graded (dg) algebra, then so does any ``pruning" of $\mathbb{F}$. In…

We extend the methods and results of [arXiv 1603.04896] to the setting of multinomial distributions satisfying certain properties. These include all the multinomial distributions arising from the direct proof of the Central Limit Theorem…