Related papers: A note on the hull and linear complementary pair o…
Motivated by entanglement-assisted quantum error-correcting codes, where the hull dimension determines the number of required pre-shared entangled pairs, we study hulls of two families of $\mathbb{F}_q$-linear codes defined by…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
Hermitian linear complementary dual codes are linear codes whose intersection with their Hermitian dual code is trivial. The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for…
The square $C^{*2}$ of a linear error correcting code $C$ is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in $C$. Squares of codes have gained attention for several applications…
An $L$-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set $L$. We show, for a fixed $\alpha,\beta>0$, that the size of any $[-1,-\beta]\cup\{\alpha\}$-spherical code is at most linear in the…
Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…
Linear complementary dual (LCD) cyclic codes were referred historically to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD…
Double circulant codes of length $2n$ over the semilocal ring $R = \mathbb{F}_q + u\mathbb{F}_q,\, u^2=u,$ are studied when $q$ is an odd prime power, and $-1$ is a square in $\mathbb{F}_q.$ Double negacirculant codes of length $2n$ are…
In \cite{anote}, Wu and Shi studied $ l $-Galois LCD codes over finite chain ring $\mathcal{R}=\mathbb{F}_q+u\mathbb{F}_q$, where $u^2=0$ and $ q=p^e$ for some prime $p$ and positive integer $e$. In this work, we extend the results to the…
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…
There is a one-to-one correspondence between $\ell$-quasi-cyclic codes over a finite field $\mathbb F_q$ and linear codes over a ring $R = \mathbb F_q[Y]/(Y^m-1)$. Using this correspondence, we prove that every $\ell$-quasi-cyclic self-dual…
For a prime power $q$, an integer $m$ and $0\leq e\leq m-1$ we study the $e$-Galois hull dimension of Gabidulin codes $G_k(\boldsymbol{\alpha})$ of length $m$ and dimension $k$ over $\mathbb{F}_{q^m}$. Using a self-dual basis…
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…
Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine. From…
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…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
Let $\mathbb{F}_{q}$ be the finite field of $q$ elements and let $D_{2n}=\langle x,y\mid x^n=1, y^2=1, yxy=x^{n-1}\rangle$ be the dihedral group of order $n$. Left ideals of the group algebra $\mathbb{F}_{q}[D_{2n}]$ are known as left…
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 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…