Related papers: Infinite families $2$-designs from binary projecti…
It has been known for a long time that $t$-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a $t$-design. While a lot of progress in the direction of…
Combinatorial $t$-designs have wide applications in coding theory, cryptography, communications and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a $t$-design. In this paper, we first…
Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It is a basic fact that the codewords of a fixed weight in a code may hold a $t$-design. Till now only a small amount of work on constructing $t$-designs…
Combinatorial $t$-designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and $t$-designs has been…
The interplay between coding theory and $t$-designs has attracted a lot of attention for both directions. It is well known that the supports of all codewords with a fixed weight in a code may hold a $t$-design. In this paper, by determining…
Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial $t$-designs have been attracted lots of research interest for decades. The interplay between coding theory and $t$-designs has…
The interplay between coding theory and $t$-designs started many years ago. While every $t$-design yields a linear code over every finite field, the largest $t$ for which an infinite family of $t$-designs is derived directly from a linear…
Three classes of binary linear codes with at most four nonzero weights were constructed in this paper, in which two of them are projective three-weight codes. As applications, $s$-sum sets for any odd $ s > 1$ were constructed.
Linear codes and $t$-designs are interactive with each other. It is well known that some $t$-designs have been constructed by using certain linear codes in recent years. However, only a small number of infinite families of the extended…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of narrow-sense BCH codes $\mathcal{C}_{(q,q+1,4,1)}$ and their dual codes with $q=2^m$ and established that the codewords of the minimum (or the second minimum) weight in these…
In this paper, we construct an infinite family of three-weight binary codes from linear codes over the ring $R=\mathbb{F}_2+v\mathbb{F}_2+v^2\mathbb{F}_2$, where $v^3=1.$ These codes are defined as trace codes. They have the algebraic…
We provide a method to construct $t$-designs from weighing matrices and association schemes. One instance of our method can produce a $3$-design from any (symmetric or skew-symmetric) conference matrix, thereby providing a partial answer to…
Coding theory and combinatorial $t$-designs have close connections and interesting interplay. One of the major approaches to the construction of combinatorial t-designs is the employment of error-correcting codes. As we all known, some…
In this paper, the 3-rank of the incidence matrices of 2-designs supported by the minimum weight codewords in a family of ternary linear codes considered in [C. Ding, C. Li, Infinite families of 2-designs and 3-designs from linear codes,…
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…
Interplay between coding theory and combinatorial $t$-designs has been a hot topic for many years for combinatorialists and coding theorists. Some infinite families of cyclic codes supporting infinite families of $3$-designs have been…
Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It was recently reported that the image sets of a fixed size of certain special polynomials may constitute a $t$-design. Till now only a small amount of…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight of this code supporting 2-designs. In this paper, we study this family of…