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Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual near MDS codes. In this paper,…
In this work, we apply the idea of composite matrices arising from group rings to derive a number of different techniques for constructing self-dual codes over finite commutative Frobenius rings. By applying these techniques over different…
In this paper we construct binary self-dual codes using the \'etale cohomology of $\mathbb{Z}/2$ on the spectra of rings of $S$-integers of global fields. We will show that up to equivalence, all self-dual codes of length at least 4 arise…
This paper explores extremal self-dual double circulant (DC) codes and linear complementary dual (LCD) codes of arbitrary length over the Galois field $\mathbb F_2$. We establish the sufficient and necessary conditions for DC codes and…
In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of…
The structure of multivariate semisimple codes over a finite chain ring $R$ is established using the structure of the residue field $\bar R$. Multivariate codes extend in a natural way the univariate cyclic and negacyclic codes and include…
In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree $n$ over a finite chain ring $ R.$ We extend the concepts of $ n $-isometry and $ n $-equivalence known for constacyclic codes to this class of…
Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their properties and existence. We show that even-like duadic…
In this paper we study duality for evaluation codes on intersections of d hypersurfaces with given d-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be…
In this paper we characterize the algebraic structure of two-dimensional $(\alpha,\beta )$-constacyclic codes of arbitrary length $s.\ell$ and of their duals. For $\alpha,\beta \in \{1,-1\}$, we give necessary and sufficient conditions for…
We propose a new systematic construction of CSS-T codes from any given CSS code using a map $\phi$. When $\phi$ is the identity map $I$, we retrieve the construction of [1] and use it to prove the existence of asymptotically good binary…
Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good.…
Let $f(u)$ and $g(v)$ be any two polynomials of degree $k$ and $\ell$ respectively ($k$ and $\ell$ are not both $1$), which split into distinct linear factors over $\mathbb{F}_{q}$. Let $\mathcal{R}=\mathbb{F}_{q}[u,v]/\langle…
In this paper we introduce self-dual cyclic and quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}. We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C^{\perp}. Since the binary image of a…
MDS codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field $F_q$ is completely solved for $q$ is…
A binary linear code $C$ is a $\mathbb{Z}_2$-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be…
In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure…
Polycyclic codes are a generalization of cyclic and constacyclic codes. Even though they have been known since 1972 and received some attention more recently, there have not been many studies on polycyclic codes. This paper presents an…
We explore the connection between simple polytopes and self-dual binary codes via the theory of small covers. We first show that a small cover $M^n$ over a simple $n$-polytope $P^n$ produces a self-dual code in the sense of Kreck-Puppe if…
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…