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Conjucyclic codes are part of a family of codes that includes cyclic, constacyclic, and quasi-cyclic codes, among others. Despite their importance in quantum error correction, they have not received much attention in the literature. This…
Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
Duadic codes are a class of cyclic codes that generalizes quadratic residue codes from prime to composite lengths. For every prime power q, we characterize the integers n such that over the finite field with q^2 elements there is a duadic…
We investigate additive codes, defined as $\mathbb{F}_q$-linear subspaces $C \subseteq \mathbb{F}_{q^h}^n$ of length $n$ and dimension $r$ over $\mathbb{F}_q$. An additive code is said to be of type $[n, r/h, d]_q^h$, where $d$ denotes the…
In this paper, we introduce a additive Tridiagonal and Double-Tridiagonal codes over $\mathbb{F}_4$ and then we study the properties of the code. Also, we find the number of additive Tridiagonal codes over $\mathbb{F}_4.$ Finally, we study…
Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes…
We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quasi-cyclic codes of index 2 with respect to the Euclidean,…
We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.
In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. For some fixed $q$, our results can produce more classes of MDS…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We study additive quaternary codes whose parameters are close to those of the extended cyclic [12; 6; 6]4-code or to the quaternary linear codes generated by the elliptic quadric in PG(3; 4) or its dual. In particular we characterize those…
Self-dual codes over finite fields and over some finite rings have been of interest and extensively studied due to their nice algebraic structures and wide applications. Recently, characterization and enumeration of Euclidean self-dual…
We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and…
A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider…
In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and…
In this paper we study the structure and properties of additive right and left polycyclic codes induced by a binary vector $a$ in $\mathbb{F}_{2}^{n}.$ We find the generator polynomials and the cardinality of these codes. We also study…
Let $\mathbb{F}_{q}$ be the finite field with $q$ elements. This paper mainly researches the polynomial representation of double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$ with $v^3=v$. Firstly, we give the…
We consider additive codes over GF(4) that are self-dual with respect to the Hermitian trace inner product. Such codes have a well-known interpretation as quantum codes and correspond to isotropic systems. It has also been shown that these…
Abelian codes and complementary dual codes form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, a family of abelian codes with complementary…