相关论文: Families of curves and weight distributions of cod…
This article introduces a method for adjusting macro-particle weights within a particle distribution while preserving statistical and physical properties. The method allows the weights of the new macro-particle distribution to be determined…
In this paper, we investigate the symbol-pair weight distributions of MDS codes and simplex codes over finite fields. Furthermore, the result shows that all the nonzero codewords of simplex codes have the same symbol $b$-weight and…
Let $q=2^n$, $0\leq k\leq n-1$, $n/\gcd(n,k)$ be odd and $k\neq n/3, 2n/3$. In this paper the value distribution of following exponential sums \[\sum\limits_{x\in \bF_q}(-1)^{\mathrm{Tr}_1^n(\alpha x^{2^{2k}+1}+\beta x^{2^k+1}+\ga…
We propose a generalization of tropical curves by dropping the rationality and integrality requirements while preserving the balancing condition. An interpretation of such curves as critical points of a certain quadratic functional allows…
We introduce the notion of families of n-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical…
Linear codes are widely studied due to their applications in communication, cryptography, quantum codes, distributed storage and many other fields. In this paper, we use the trace and norm functions over finite fields to construct a family…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
Orbit codes are a family of codes employable for communications on a random linear network coding channel. The paper focuses on the classification of these codes. We start by classifying the conjugacy classes of cyclic subgroups of the…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
A new family of distributions on the circle is introduced which are a generalization of the Cardioid distributions. The elementary properties such as mean, variance and the characteristic function are computed. The distribution is either…
In this article we study the automorphism groups of binary cyclic codes. In particular, we provide explicit constructions for codes whose automorphism groups can be described as (a) direct products of two symmetric groups or (b) iterated…
A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo $2^{m}$ is a linear code with property that if the codeword $(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift $(c_1,c_2,...,c_0)\in \mathcal{C}$.…
Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, some kinds of p-ary linear codes with few weights are constructed by use of the given de ning set,…
We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces,…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
We study families of rational curves on an algebraic variety satisfying incidence conditions. We prove an analogue of bend-and-break: that is, we show that under suitable conditions, such a family must contain reducibles. In the case of…
This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about…