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Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer $[\frac{q^k-1}{q-1},k…

Information Theory · Computer Science 2024-08-20 Xu Pan , Hao Chen , Hongwei Liu , Shengwei Liu

We discuss the problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties and, more generally, to Schubert varieties in Grassmannians. The problem is partially solved in the case…

Combinatorics · Mathematics 2009-11-06 Sudhir R. Ghorpade , Arunkumar R. Patil , Harish K. Pillai

Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide…

Combinatorics · Mathematics 2023-01-24 Daniele Bartoli , Martino Borello

We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…

Optimization and Control · Mathematics 2016-10-20 Daniel Bienstock , Gonzalo Munoz

Recently some mixed alphabet rings are involved in constructing few-Lee weight additive codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring…

Information Theory · Computer Science 2022-06-07 Pramod Kumar Kewat , Nilay Kumar Mondal

We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…

Optimization and Control · Mathematics 2014-02-11 C. H. Jeffrey Pang

We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…

Computational Complexity · Computer Science 2026-05-19 Noé Demange , Yann Strozecki

Quantum error-correcting codes (QECCs) require high encoding rate in addition to high threshold unless a sufficiently large number of physical qubits are available. The many-hypercube (MHC) codes defined as the concatenation of the…

Quantum Physics · Physics 2026-01-19 Ryota Nakai , Hayato Goto

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…

Information Theory · Computer Science 2024-01-05 Somphong Jitman

This paper is devoted to the generalization of the construction of minimal varieties from the previous work of Meng Chen, Chen Jiang and Binru Li. We first establish several effective nefness criterions for the canonical divisor of weighted…

Algebraic Geometry · Mathematics 2025-07-15 Pinxian Bie

In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, which were recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking…

Information Theory · Computer Science 2020-04-28 Chunming Tang , Yan Qiu , Qunying Liao , Zhengchun Zhou

Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, we determined the complete weight enumerator of two classes of p-ary linear codes constructed from defining set.…

Information Theory · Computer Science 2015-12-24 Qiuyan Wang , Fei Li , Kelan Ding , Dongdai Lin

Multi-class classification is mandatory for real world problems and one of promising techniques for multi-class classification is Error Correcting Output Code. We propose a method for constructing the Error Correcting Output Code to obtain…

Machine Learning · Computer Science 2013-12-30 Patoomsiri Songsiri , Thimaporn Phetkaew , Ryutaro Ichise , Boonserm Kijsirikul

Subfield codes of linear codes over finite fields have recently received much attention. Some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, the $q$-ary…

Information Theory · Computer Science 2023-03-08 Li Xu , Cuiling Fan , Sihem Mesnager , Rong Luo , Haode Yan

Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…

Information Theory · Computer Science 2018-08-14 Sihem Mesnager , Ahmet Sınak

We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\mathbb{F}_2 +v\mathbb{F}_2 +v^2\mathbb{F}_2 +v^3\mathbb{F}_2 +v^4\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic…

Information Theory · Computer Science 2017-01-05 Yan Liu , Minjia Shi , Patrick Solé

Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…

Information Theory · Computer Science 2020-03-18 Yansheng Wu , Yoonjin Lee

Recently, constructions of optimal linear codes from simplicial complexes have attracted much attention and some related nice works were presented. Let $q$ be a prime power. In this paper, by using the simplicial complexes of ${\mathbb…

Information Theory · Computer Science 2024-07-16 Bing Chen , Yunge Xu , Zhao Hu , Nian Li , Xiangyong Zeng

Minimal linear codes are algebraic objects which gained interest in the last twenty years, due to their link with Massey's secret sharing schemes. In this context, Ashikhmin and Barg provided a useful and a quite easy to handle sufficient…

Information Theory · Computer Science 2019-12-09 Matteo Bonini , Martino Borello

Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…

Combinatorics · Mathematics 2020-04-30 Daniele Bartoli , Matteo Bonini , Marco Timpanella