Related papers: A tight upper bound on the number of non-zero weig…
Let $\mathbb{F}_q$ be a finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(\gamma,\Delta)$-cyclic codes over a class of finite non-chain commutative rings…
In this paper we introduce the notion of $\lambda$-constacyclic codes over finite rings $R$ for arbitary element $\lambda$ of $R$. We study the non-invertible-element constacyclic codes (NIE-constacyclic codes) over finite principal ideal…
Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic…
Cosmological neutrino mass and abundance measurements are reaching unprecedented precision. Testing their stability versus redshift and scale is a crucial issue, as it can serve as a guide for optimizing ongoing and future searches. Here,…
Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band…
Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. In this paper, we derive necessary and sufficient conditions under which two torsion elements in $\mathrm{Mod}(S_g)$ will have…
Given a skew diagram $\gamma/\lambda$, we determine a set of lower and upper bounds that a partition $\mu$ must satisfy for Littlewood-Richards coefficients $c^{\gamma}_{\lambda,\mu}>0$. Our algorithm depends on the characterization of…
We study the nonabelian composition factors of a finite group $G$ assumed to admit an $\operatorname{Aut}(G)$-orbit of length at least $\rho|G|$, for a given $\rho\in\left(0,1\right]$. Our main results are the following: The orders of the…
We consider the problem of untangling a given (non-planar) straight-line circular drawing $\delta_G$ of an outerplanar graph $G=(V, E)$ into a planar straight-line circular drawing by shifting a minimum number of vertices to a new position…
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. Most previous results obtained so far were for cyclic codes with no more than three zeroes. Inspired by the works…
This paper gives a unified algebraic solution to seven open problems of Wang, Tang and Ding on cyclic, negacyclic and constacyclic codes supporting designs. For the cyclic code \[ C\left(\frac{p^s-1}{2},\frac{p^s+1}{2}\right), \] a Cayley…
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that…
In this paper, we introduce a class of functions that assume only a limited number $\lambda$ of values within a given Hamming $\rho$-ball and call them locally $(\rho, \lambda)$-bounded functions. We develop function-correcting codes (FCCs)…
Let $r,s,t$ be three positive integers and $\mathcal{C}$ be a binary linear code of lenght $r+s+t$. We say that $\mathcal{C}$ is a triple cyclic code of lenght $(r,s,t)$ over $\mathbb{Z}_2$ if the set of coordinates can be partitioned into…
For a family $\mathcal{F}$ of graphs, let $ex(n,\mathcal{F})$ denote the maximum number of edges in an $n$-vertex graph which contains none of the members of $\mathcal{F}$ as a subgraph. A longstanding problem in extremal graph theory asks…
We investigate the \emph{minimum weight cycle (MWC)} problem in the $\mathsf{CONGEST}$ model of distributed computing. For undirected weighted graphs, we design a randomized algorithm that achieves a $(k+1)$-approximation, for any…
In chameleon $f(R)$-gravity, the fifth force will lead to `upturns' in galaxy rotation curves near the screening radius. The location of the upturn depends on the cosmic background value of the scalar field $f_{R0}$, as well as the mass,…
High-rate bivariate bicycle (BB) codes are promising low-overhead quantum memories, but their stabilizer checks typically have weight $6$ or higher, making syndrome extraction challenging. We introduce subsystem bivariate bicycle (SBB)…
In this paper, we study the $\sigma$-self-orthogonality of constacyclic codes of length $p^s$ over the finite commutative chain ring $\mathbb F_{p^m} + u \mathbb F_{p^m}$, where $u^2=0$ and $\sigma$ is a ring automorphism of $\mathbb…
We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. Its shape is a direct generalization of the classical…