相关论文: Stanley-Reisner resolution of constant weight line…
Perturbations of the linearized vacuum Einstein equations on a null cone in the Bondi-Sachs formulation of General Relativity can be derived from a single master function with spin weight two, which is related to the Weyl scalar \Psi_0, and…
Special functions, coding theory and $t$-designs have close connections and interesting interplay. A standard approach to constructing $t$-designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the…
We extend the recently much-studied two-weight commutator estimates to the multilinear setting. In contrast to previous results, our result respects the multilinear nature of the problem fully and is formulated with the genuinely…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Star configurations are certain unions of linear subspaces of projective space that have been studied extensively. We develop a framework for studying a substantial generalization, which we call matroid configurations, whose ideals…
For a family of polynomials in two continuous variables, orthogonal with respect to a weight function, we prove, under suitable conditions, the equivalence of the following properties: the matrix Pearson equation of the weight, the second…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner's symmetral…
In this paper we study weighted singular $p$-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied. Based on Nehari manifolds we prove the…
This article gives a new upper bound for the resurgence number of symbolic powers of matroidal configuration in the following situations: the height of the matroidal configuration is big, or the height is small, and the corresponding…
We provide a general approach to the classification results of stable solutions of (possibly nonlinear) elliptic problems with Robin conditions. The method is based on a geometric formula of Poincar\'e type, which is inspired by a classical…
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their…
We introduce the notion of sum-matroids and show its association with sum-rank metric codes. As a consequence, some results for sum-rank metric codes by Mart\'inez-Pe\~nas are generalized for sum-matroids. The sum-matroids generalize 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…
We derive a general lower bound for the generalized Hamming weights of nested matrix-product codes, with a particular emphasis on the cases with two and three constituent codes. We also provide an upper bound which is reminiscent of the…
We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher…
In this work we study a weak order ideal associated with the coset leaders of a non-binary linear code. This set allows the incrementally computation of the coset leaders and the definitions of the set of leader codewords. This set of…
We present an approach to showing that a linear code is resilient to random errors. We use this approach to obtain decoding results for both transitive codes and Reed-Muller codes. We give three kinds of results about linear codes in…