相关论文: On linear codes from maximal curves

We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…

Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a…

Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…

Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…

We define a class of automorphisms of rational function fields of finite characteristic and employ these to construct different types of optimal linear rank-metric codes. The first construction is of generalized Gabidulin codes over…

As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…

The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…

In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…

Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…

Based on results in finite geometry we prove the existence of MRD codes in (F_q)_(n,n) with minimum distance n which are essentially different from Gabidulin codes. The construction results from algebraic structures which are closely…

We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the…

In this paper we compute the order (or Feng-Rao) bound on the minimum distance of one-point algebraic geometry codes, when the Weierstrass semigroup at the point Q is an Arf semigroup. The results developed to that purpose also provide the…

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…

The construction of Maximum Distance Profile (MDP) convolutional codes in general requires the use of very large finite fields. In contrast convolutional codes with optimal column distances maximize the column distances for a given…

This preprint is of a chapter to appear in {\it Combinatorics and finite fields: Difference sets, polynomials, pseudorandomness and applications. Radon Series on Computational and Applied Mathematics}, K.-U. Schmidt and A. Winterhof (eds.).…

This paper provides new constructions and lower bounds for subspace codes, using Ferrers diagram rank-metric codes from matchings of the complete graph and pending blocks. We present different constructions for constant dimension codes with…

Motivated by Xing's method [7], we show that there exist [n,k,d] linear Hermitian codes over F_{q^2} with k+d>=n-3 for all sufficiently large q. This improves the asymptotic bound of Algebraic-Geometry codes from Hermitian curves given in…

In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and…

This paper investigates the construction of rank-metric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension…