Related papers: MDS linear codes with one dimensional hull
There has been recent interest in the study of shortest self-orthogonal embeddings of binary linear codes, since many such codes are optimal self-orthogonal codes. Several authors have studied the length of a shortest self-orthogonal…
A simple and general definition of quasi cyclic low density parity check (QC LDPC) codes which are constructed based on circulant permutation matrices (CPM) is proposed. As an special case of this definition, we first represent one type of…
Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we…
We investigate a natural subfamily of twisted linearized Reed--Solomon (TLRS) codes in the sum-rank metric, where the twist is applied only to the constant term. We establish a simple necessary and sufficient condition for these codes to be…
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…
We present five new infinite families of linear near-MDS codes uniformly packed in the wide sense (UPWS). These codes are also almost perfect multiple coverings of the deep holes or farthest-off points (APMCF), i.e.\ the vectors lying at…
Recently, subfield codes of geometric codes over large finite fields $\gf(q)$ with dimension $3$ and $4$ were studied and distance-optimal subfield codes over $\gf(p)$ were obtained, where $q=p^m$. The key idea for obtaining very good…
We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual code by means of unitary matrices, where some of them generalize the quadratic double circulant constructions.…
A code is a subset of the vertex set of a Hamming graph. The set of $s$-neighbours of a code is the set of all vertices at Hamming distance $s$ from their nearest codeword. A code $C$ is $s$-elusive if there exists a distinct code $C'$ that…
Both MDS and Euclidean self-dual codes have theoretical and practical importance and the study of MDS self-dual codes has attracted lots of attention in recent years. In particular, determining existence of $q$-ary MDS self-dual codes for…
A code of length $n$ is said to be (combinatorially) $(\rho,L)$-list decodable if the Hamming ball of radius $\rho n$ around any vector in the ambient space does not contain more than $L$ codewords. We study a recently introduced class of…
We prove that if $n >k^2$ then a $k$-dimensional linear code of length $n$ over ${\mathbb F}_{q^2}$ has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length $2^m-1$…
We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…
In this paper, we introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are not invariants of the matroid (for a linear block code) or…
Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) from Calderbank-Shor-Steane (CSS) construction. In general, it's difficult to determine the required number of…
Linear complementary dual (LCD) codes is a class of linear codes introduced by Massey in 1964. LCD codes have been extensively studied in literature recently. In addition to their applications in data storage, communications systems, and…
Generalizing the linear complementary duals, the linear complementary pairs and the hull of codes, we introduce the concept of $\ell$-dimension linear intersection pairs ($\ell$-DLIPs) of codes over a finite commutative ring $(R)$, for some…
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…