Related papers: Minimal linear codes from characteristic functions
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…
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 study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
In this paper, we consider minimal linear codes in a general construction of linear codes from q-ary functions. First, we give the sufficient and necessary condition for codewords to be minimal. Second, as an application, we present four…
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…
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…
Let $k\leq n$ be two positive integers and $q$ a prime power. The basic question in minimal linear codes is to determine if there exists an $[n,k]_q$ minimal linear code. The first objective of this paper is to present a new sufficient and…
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 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…
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research…
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…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
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…
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…
The study on minimal linear codes has received great attention due to their significant applications in secret sharing schemes and secure two-party computation. Until now, numerous minimal linear codes have been discovered. However, to the…
Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In…
Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
We provide new families of minimal codes in any characteristic. Also, an inductive construction of minimal codes is presented.