Related papers: Two classes of LCD codes derived from $(\mathcal{L…
Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed-Solomon and Gabidulin codes are…
Double Toeplitz (DT) codes are codes with a generator matrix of the form $(I,T)$ with $T$ a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When $T$ is tridiagonal and symmetric we determine its spectrum…
Polycyclic codes offer a natural generalization of cyclic codes and provide a broader algebraic framework for constructing linear codes with good parameters. In this paper, we study binary polycyclic codes associated with powers of…
Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The constructed…
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank…
We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.
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…
We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the…
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 large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
In this work, we propose two criteria for linear codes obtained from the Plotkin sum construction being symplectic self-orthogonal (SO) and linear complementary dual (LCD). As specific constructions, several classes of symplectic SO codes…
Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…
An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters [n,k,d] and the list size L. L-MDS codes are then defined as codes that attain this bound (under a slightly…
Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed…
Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a…
In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with…
Let $\mathbb{F}_{q}$ denote the finite field of order $q,$ let $m_1,m_2,\cdots,m_{\ell}$ be positive integers satisfying $\gcd(m_i,q)=1$ for $1 \leq i \leq \ell,$ and let $n=m_1+m_2+\cdots+m_{\ell}.$ Let…
In this paper, we first consider the iterated skew polynomial ring $\mathscr{R}[z_1;\tau_1,\delta_{\tau_1}]$\\$[z_2;\tau_2,\delta_{\tau_2}]$, where $\mathscr{R}$ is a finite ring with unity. Then we use this structure for the construction…
The paper has a threefold purpose. The first purpose is to present an explicit description of expanded cyclic codes defined in $\GF(q^m)$. The proposed explicit construction of expanded generator matrix and expanded parity check matrix…
Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable…