Related papers: The second generalized Hamming weight of some eval…
A connected matching in a graph G consists of a set of pairwise disjoint edges whose covered vertices induce a connected subgraph of G. While finding a connected matching of maximum cardinality is a well-solved problem, it is NP-hard to…
We compute the integral torus-equivariant cohomology ring for weighted projective space for two different torus actions by embedding the cohomology in a sum of polynomial rings $\oplus_{i=0}^n \Z[t_1, t_2,..., t_n]$. One torus action gives…
We study the functional codes $C_2(X)$ defined on projective varieties $X$, in the case where $X\subset \mathbb{P}^3$ is a 1-degenerate quadric or a non-degenerate quadric (hyperbolic or elliptic). We find the minimum distance of these…
We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if the vertex codes have minimum distance $\ge 3$, the overall…
It was recently shown that RGHW (relative generalized Hamming weight) exactly expresses the security of linear ramp secret sharing scheme. In this paper we determine the true value of the asymptotic metric for RGHW previously proposed by…
In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on ${n}$ vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
Let $p$ be a prime number, $q=p^s$ for a positive integer $s$. For any positive divisor $e$ of $q-1$, we construct an infinite family codes of size $q^{2m}$ with few Lee-weight. These codes are defined as trace codes over the ring…
Just as the Hamming weight spectrum of a linear block code sheds light on the performance of a maximum likelihood decoder, the pseudo-weight spectrum provides insight into the performance of a linear programming decoder. Using properties of…
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network, which restricts…
The weight hierarchy of one-point algebraic geometry codes can be estimated by means of the generalized order bounds, which are described in terms of a certain Weierstrass semigroup. The asymptotical behaviour of such bounds for r > 1…
In this paper, we provide conditions that hulls of generalized Reed-Solomon (GRS) codes are also GRS codes from algebraic geometry codes. If the conditions are not satisfied, we provide a method of linear algebra to find the bases of hulls…
In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…
A two-dimensional nonlinear gauge theory that can be proposed for generalization to higher dimensions is derived by means of cohomological arguments.
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
The node set of a two-mode network consists of two disjoint subsets and all its links are linking these two subsets. The links can be weighted. We developed a new method for identifying important sub-networks in two-mode networks. The…
A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the…
A new and easy way of deriving Gauss's Generalized Hypergeometric Theorem is presented by using the Bilateral Binomial Theorem.
We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus,…