Related papers: Minimal Linear Codes over Finite Fields
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, a class of $q$-ary linear codes with few weights are presented and their weight distributions are determined using Gauss periods. Some of…
J. Y. Hyun, et al. (Des. Codes Cryptogr., vol. 88, pp. 2475-2492, 2020) constructed some optimal and minimal binary linear codes generated by one or two order ideals in hierarchical posets of two levels. At the end of their paper, they left…
In this paper, we construct a large family of projective linear codes over ${\mathbb F}_{q}$ from the general simplicial complexes of ${\mathbb F}_{q}^m$ via the defining-set construction, which generalizes the results of [IEEE Trans. Inf.…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
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…
In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain…
Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes…
The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…
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…
We consider binary abelian codes of length $p^m q^n$, where $p$ and $q$ are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…
In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal…
A generator matrix of a linear code $\C$ over $\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\gf(q^\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\gf(q^\ell)$,…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…
Minimal codewords have applications in decoding linear codes and in cryptography. We study the maximum number of minimal codewords in binary linear codes of a given length and dimension. Improved lower and upper bounds on the maximum number…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…