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It is well known that the problem of determining the weight distributions of families of cyclic codes is, in general, notoriously difficult. An even harder problem is to find characterizations of families of cyclic codes in terms of their…
In this article, we construct linear codes over the commutative non-unital ring $I$ of size four. We obtain their Lee-weight distributions and study their binary Gray images. Under certain mild conditions, these classes of binary codes are…
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…
Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…
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…
Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their…
Subfield codes of linear codes over finite fields have recently received much attention. Some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, the $q$-ary…
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…
The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}:…
Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…
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…
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
Few-weight codes over finite chain rings are associated with combinatorial objects such as strongly regular graphs (SRGs), strongly walk-regular graphs (SWRGs) and finite geometries, and are also widely used in data storage systems and…
Combinatorial designs are closely related to linear codes. In recent year, there are a lot of $t$-designs constructed from certain linear codes. In this paper, we aim to construct $2$-designs from binary three-weight codes. For any binary…
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we present the explicit complete weight enumerator of a family of $p$-ary linear codes constructed with defining…
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…
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…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
It is known that a linear two-weight code $C$ over a finite field $\F_q$ corresponds both to a multiset in a projective space over $\F_q$ that meets every hyperplane in either $a$ or $b$ points for some integers $a<b$, and to a strongly…