Related papers: Good Codes From Dihedral Groups
A systematic way of constructing Grassmannian codes endowed with the subspace distance as lifts of matrix codes over the prime field $GF(p)$ is introduced. The matrix codes are $GF(p)$-subspaces of the ring $M_2(GF(p))$ of $2 \times 2$…
In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ring, where the ring is a finite commutative Frobenius ring…
Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent…
We formulate explicit predictions concerning the symmetry of optimal codes in compact metric spaces. This motivates the study of optimal codes in various spaces where these predictions can be tested.
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…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…
We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples…
This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…
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…
We define and study a class of Reed-Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases.
In the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon…
We present a simple method to establish the existence of asymptotically good sequences of iso-dual AG-codes. A key advantage of our approach, beyond its simplicity, is its flexibility, allowing it to be applied to a wide range of towers of…
Two isometry groups of combinatorial codes are described: the group of automorphisms and the group of monomial automorphisms, which is the group of those automorphisms that extend to monomial maps. Unlike the case of classical linear codes,…
From a given $[n, k]$ code $C$, we give a method for constructing many $[n, k]$ codes $C'$ such that the hull dimensions of $C$ and $C'$ are identical. This method can be applied to constructions of both self-dual codes and linear…
Employing isomorphisms between their ambient rings, we propose new definitions of equivalence and isometry for skew polycyclic codes that will lead to tighter classifications than existing ones. This reduces the number of previously known…
Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of…
We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In…
The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. This paper focuses on optimal two-dimensional optical orthogonal codes with autocorrelation and cross-correlation…
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…
Let $F=\mathbb{F}_q$ and let $K=\mathbb{F}_{q^m}$ be a finite extension. An additive left group code is a left $FG$-submodule of the group algebra $KG$. In this paper, we introduce projector additive left group codes and restricted…