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A new method of constructing optimum constant weight codes over F_2 based on a generalized $(u, u+v)$ construction is presented. We present a new method of constructing superimposed code $C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$…

Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…

In this manuscript, we work over the non-chain ring $\mathcal{R} = \mathbb{F}_2[u]/\langle u^3 - u\rangle $. Let $m\in \mathbb{N}$ and let $L, M, N \subseteq [m]:=\{1, 2, \dots, m\}$. For $X\subseteq [m]$, define $\Delta_X:=\{v \in…

Maximum distance separable (MDS) codes are considered optimal because the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are likely the generalized Reed-Solomon (GRS) codes. In 1989, Roth…

Locally repairable codes which are optimal with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known…

One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…

In this paper, we consider the construction of linear lexicodes over finite chain rings by using a $B$-ordering over these rings and a selection criterion. % and a greedy Algorithm. As examples we give lexicodes over $\mathbb{Z}_4$ and…

In classical coding theory, it is common to construct new codes via propagation rules. There are various propagation rules to construct classical block codes. However, propagation rules have not been extensively explored for constructions…

We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…

The binary Hamming codes with parameters $[2^m-1, 2^m-1-m, 3]$ are perfect. Their extended codes have parameters $[2^m, 2^m-1-m, 4]$ and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes…

Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory,…

Let $\text{AGL}(1,\Bbb F_q)$ be the affine linear group of dimension $1$ over a finite field $\Bbb F_q$. $\text{AGL}(1,\Bbb F_q)$ acts sharply 2-transitively on $\Bbb F_q$. Given $S<\text{AGL}(1,\Bbb F_q)$ and an integer $k$ with $1\le k\le…

This paper investigates fundamental properties of nonlinear binary codes by looking at the codebook matrix not row-wise (codewords), but column-wise. The family of weak flip codes is presented and shown to contain many beautiful properties.…

Subspace codes, and in particular cyclic subspace codes, have gained significant attention in recent years due to their applications in error correction for random network coding. In this paper, we introduce a new technique for constructing…

Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…

In ``Infinite families of near MDS codes holding $t$-designs, IEEE Trans. Inform. Theory, 2020, 66(9), pp. 5419-5428'', Ding and Tang made a breakthrough in constructing the first two infinite families of NMDS codes holding $2$-designs or…

Constacyclic codes over finite fields are of theoretical importance as they are closely related to a number of areas of mathematics such as algebra, algebraic geometry, graph theory, combinatorial designs and number theory. However, the…

Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…

A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements…

In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, which were recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking…