Related papers: MDS linear codes with one dimensional hull
The Euclidean hull of a linear code $C$ is the intersection of $C$ with its Euclidean dual $C^\perp$. The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the…
The hull of a linear code is defined as the intersection of the code and its dual. This concept was initially introduced to classify finite projective planes. The hull plays a crucial role in determining the complexity of algorithms used to…
The Euclidean hull of a linear code $C$ is defined as $C\cap C^{\perp}$, where $C^\perp$ denotes the dual of $C$ under the Euclidean inner product. A linear code with zero hull dimension is called a linear complementary dual (LCD) code. A…
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 a linear code $C$ is the intersection of $C$ with its dual code. We present and analyze the number of linear $q$-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given…
The hull of a linear code is defined to be the intersection of the code and its dual. When the size of the hull is small, it has been proved that some algorithms for checking permutation equivalence of two linear codes and computing the…
The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect…
The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and information protection. Linear codes with the smallest hull are…
The intersection ${\bf C}\bigcap {\bf C}^{\perp}$ (${\bf C}\bigcap {\bf C}^{\perp_h}$) of a linear code ${\bf C}$ and its Euclidean dual ${\bf C}^{\perp}$ (Hermitian dual ${\bf C}^{\perp_h}$) is called the Euclidean (Hermitian) hull of this…
Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have been utilized as ingredients to construct…
The hull of a linear code over finite fields is the intersection of the code and its dual, which was introduced by Assmus and Key. In this paper, we develop a method to construct linear codes with trivial hull ( LCD codes) and…
In this paper, we introduce a general construction of linear codes with small dimension hull from any non LCD codes. Furthermore, we show that for any linear code $\Co$ over $\F_q$ ($q > 3$) with $dim(Hull(\Co))=h$ there exist an equivalent…
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…
The hull $H(C)$ of a linear code $C$ is defined by $H(C)=C \cap C^\perp$. A linear code with a complementary dual (LCD) is a linear code with $H(C)=\{0\}$. The dimension of the hull of a code is an invariant under permutation equivalence.…
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…
In this paper, we study Euclidean and Hermitian hulls of generalized Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the Hermitian hulls of Roth-Lempel typed codes. We present explicit constructions of MDS and AMDS…
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…
Hulls of linear codes have been of interest and extensively studied due to their rich algebraic structures and wide applications. In this paper, alternative characterizations of hulls of linear codes are given as well as their applications.…
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…
The hull of a linear code $C$ is the intersection of $C$ with its dual. To the best of our knowledge, there are very few constructions of binary linear codes with the hull dimension $\ge 2$ except for self-orthogonal codes. We propose a…