Related papers: Sixteen New Linear Codes With Plotkin Sum
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…
Matrix product codes are generalizations of some well-known constructions of codes, such as Reed-Muller codes, $[u+v,u-v]$-construction, etc. Recently, a bound for the symbol-pair distance of a matrix product code was given in \cite{LEL},…
In this work, we propose two criteria for linear codes obtained from the Plotkin sum construction being symplectic self-orthogonal (SO) and linear complementary dual (LCD). As specific constructions, several classes of symplectic SO codes…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put forward a new method to construct minimal linear codes by…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
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…
Given two binary codes of length n, using Plotkin construction we obtain a code of length 2n. The construction works for linear and nonlinear codes. For the linear case, it is straightforward to see that the dimension of the final code is…
In this paper we introduce a new type of code, called projective nested cartesian code. It is obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $\mathbb{P}^n(\mathbb{F}_q)$, and they may be seen…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
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…
We construct new linear codes with high minimum distance d. In at least 12 cases these codes improve the minimum distance of the previously known best linear codes for fixed parameters n,k. Among these new codes there is an optimal ternary…
This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…
The current best known $[239, 21], \, [240, 21], \, \text{and} \, [241, 21]$ binary linear codes have minimum distance 98, 98, and 99 respectively. In this article, we introduce three binary Goppa codes with Goppa polynomials $(x^{17} +…
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…
Constant dimension codes are e.g. used for error correction and detection in random linear network coding, so that constructions for these codes have achieved wide attention. Here, we improve over 150 lower bounds by describing better…
Constructions of distance-optimal codes and quasi-perfect codes are challenging problems and have attracted many attentions. In this paper, we give the following three results. 1) If $\lambda|q^{sm}-1$ and $\lambda…
Constructions of optimal locally repairable codes (LRCs) achieving Singleton-type bound have been exhaustively investigated in recent years. In this paper, we consider new bounds and constructions of Singleton-optimal LRCs with minmum…
We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…
We provide new families of minimal codes in any characteristic. Also, an inductive construction of minimal codes is presented.