Related papers: Intersection of linear and multi-twisted codes wit…
QR decomposition is an essential operation for solving linear equations and obtaining least-squares solutions. In high-performance computing systems, large-scale parallel QR decomposition often faces node faults. We address this issue by…
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…
In this paper, we prove a formula of Grauert-Riemenschneider canonical sheaf and log canonical thresholds for a general residual intersection as well as an equality of minimal log discrepancies under a general link. We also prove an…
Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…
In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In…
Support constrained generator matrix for a linear code has been an active topic in recent years. The necessary and sufficient condition for the existence of MDS codes over small fields with support constrained generator matrices were…
In this paper, we introduce a standard generator matrix for mixed-alphabet linear codes over finite chain rings. Furthermore, we show that, when one has a linear complementary pair (LCP) of mixed-alphabet linear codes, both codes are…
We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matrices and establish necessary and sufficient conditions…
Given $\texttt{S}|\texttt{R}$ a finite Galois extension of finite chain rings and $\mathcal{B}$ an $\texttt{S}$-linear code we define two Galois operators, the closure operator and the interior operator. We proof that a linear code is…
This paper considers the problem of designing maximum distance separable (MDS) codes over small fields with constraints on the support of their generator matrices. For any given $m\times n$ binary matrix $M$, the GM-MDS conjecture, due to…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…
Maximum distance separable (in short, MDS), near MDS (in short, NMDS), and self-orthogonal codes play a pivotal role in algebraic coding theory, particularly in applications such as quantum communications and secret sharing scheme.…
Self-dual MDS and NMDS codes over finite fields are linear codes with significant combinatorial and cryptographic applications. In this paper, firstly, we investigate the duality properties of generalized twisted Reed-Solomon (abbreviated…
We construct two series of linear codes over finite ring $\mathbb{F}_{q}[x]/(x^2)$ and Galois ring $GR(p^2,m)$ respectively reaching the Griesmer bound. They derive two series of codes over finite field $\mathbb{F}_{q}$ by Gray map. The…
Generalized Matrix Chains (GMCs) are products of matrices where each matrix carries features (e.g., general, symmetric, triangular, positive-definite) and is optionally transposed and/or inverted. GMCs are commonly evaluated via sequences…
Galois field (GF) arithmetic circuits find numerous applications in communications, signal processing, and security engineering. Formal verification techniques of GF circuits are scarce and limited to circuits with known bit positions of…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
Twisted generalized Reed-Solomon (TGRS) codes are an extension of the generalized Reed-Solomon (GRS) codes by adding specific twists, which attract much attention recently. This paper presents an in-depth and comprehensive investigation of…
For a grading-restricted vertex superalgebra $V$ and an automorphism $g$ of $V$, we give a linearly independent set of generators of the universal lower-bounded generalized $g$-twisted $V$-module $\widehat{M}^{[g]}_{B}$ constructed by the…