Related papers: Quaternary codes with new parameters from two-gene…
We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F_2 + uF_2 and F_4 + uF_4; using groups of order 3, 7, 9, 13, and 15.…
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…
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.
In this paper, we construct an infinite family of five-weight codes from trace codes over the ring $R=\mathbb{F}_2+u\mathbb{F}_2$, where $u^2=0.$ The trace codes have the algebraic structure of abelian codes. Their Lee weight is computed by…
Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first…
Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that…
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…
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…
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…
One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…
We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring $\mathbb{F}_p+u\mathbb{F}_p+v\mathbb{F}_p+uv\mathbb{F}_p,$ where $u^2=0,v^2=0,uv=vu.$ These codes are defined as trace codes. They have the…
Generalized Bicycle (GB) codes offer a compelling alternative to surface codes for quantum error correction. This paper focuses on (2,2)-Generalized Bicycle codes, constructed from pairs of binary circulant matrices with two non-zero…
A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In…
R. W. Hamming published the Hamming codes and the sphere packing bound in 1950. In the past 75 years, infinite families of distance-optimal linear codes over finite fields with minimum distance at most 8 with respect to the sphere packing…
In this paper new infinite families of linear binary completely transitive codes are presented. They have covering radius $\rho = 3$ and 4, and are a half part of the binary Hamming and the binary extended Hamming code of length $n=2^m-1$…
Research on codes over finite rings has intensified since the discovery in 1994 of the fact that some best binary non-linear codes can be obtained as images of $\mathbb{Z}_4$-linear codes. Codes over many different finite rings has been a…
Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let $\alpha $ be a generator of…
Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of…