相关论文: The two-sided Galois duals of multi-twisted codes
We begin this chapter by introducing the simple algebraic structure of cyclic codes over finite fields. This structure undergoes a series of generalizations to present algebraic descriptions of constacyclic, quasi-cyclic (QC), quasi-twisted…
In this study, we consider the Euclidean and Galois hulls of multi-twisted (MT) codes over a finite field $\mathbb{F}_{p^e}$ of characteristic $p$. Let $\mathbf{G}$ be a generator polynomial matrix (GPM) of a MT code $\mathcal{C}$. For any…
In this paper, we derive a formula for constructing a generator matrix for the intersection of any pair of linear codes over a finite field. Consequently, we establish a condition under which a linear code has a trivial intersection with…
In recent literature, matrix product (MP) codes and their duals have gained significant attention due to their application in the construction of quantum stabilizer codes. In this paper, we begin with providing a formula that characterizes…
The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these years. In this paper, we study Galois hulls of linear codes. Firstly, the symmetry of the…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right…
In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and…
Generalizing Euclidean inner product and Hermitian inner product, we introduce Galois inner products, and study the Galois self-dual constacyclic codes in a very general setting by a uniform method. The conditions for existence of Galois…
Maximum distance separable (MDS) codes that are not equivalent to generalized Reed-Solomon (GRS) codes are called non-GRS MDS codes. Alongside near MDS (NMDS) codes, they are applicable in communication, cryptography, and storage systems.…
The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls of linear codes. In this paper, we study the Galois hulls of (extended) GRS codes and present several new constructions of MDS codes with Galois…
Let $q=p^m$ be a prime power and $e$ be an integer with $0\leq e\leq m-1$. $e$-Galois self-dual codes are generalizations of Euclidean $(e=0)$ and Hermitian ($e=\frac{m}{2}$ with even $m$) self-dual codes. In this paper, for a linear code…
In this paper, we study quasi-twisted codes and their relationship with additive constacyclic codes through a polynomial-based approach. We first present a polynomial characterization of quasi-twisted codes over finite fields analogous to…
The hull of a linear code is the intersection of itself with its dual code with respect to certain inner product. Both Euclidean and Hermitian hulls are of theorical and practical significance. In this paper, we construct several new…
The hull of linear codes plays an important role in quantum information and coding theory. In the present paper, by investigating the Galois hulls of generalized Reed-Solomon (GRS) codes and extended GRS codes over the finite field Fq, we…
Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes…
We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising…
Linear complementary pairs (LCP) of codes play an important role in armoring implementations against side-channel attacks and fault injection attacks. One of the most common ways to construct LCP of codes is to use Euclidean linear…
Interest in the hulls of linear codes has been growing rapidly. More is known when the inner product is Euclidean than Hermitian. A shift to the latter is gaining traction. The focus is on a code whose Hermitian hull dimension and dual…
Multi-twisted (MT) codes were introduced as a generalization of quasi-twisted (QT) codes. QT codes have been known to contain many good codes. In this work, we show that codes with good parameters and desirable properties can be obtained…