Related papers: Symplectic self-orthogonal quasi-cyclic codes
In this paper we construct, using GAP System for Computational Discrete Algebra, some cyclic subspace codes, specially an optimal code over the finite field F_{2^{10}}. Further we present a definition and an example of the $q$-analogous of…
Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field…
Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension and minimum distance, in analogy…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R=1/2, by our constructive lower bound,…
A code $C \colon \{0,1\}^k \to \{0,1\}^n$ is a $q$-locally decodable code ($q$-LDC) if one can recover any chosen bit $b_i$ of the message $b \in \{0,1\}^k$ with good confidence by randomly querying the encoding $x := C(b)$ on at most $q$…
Constructions of distance-optimal codes and quasi-perfect codes are challenging problems and have attracted many attentions. In this paper, we give the following three results. 1) If $\lambda|q^{sm}-1$ and $\lambda…
Recent work has shown that properly designed protograph-based LDPC codes may have minimum distance linearly increasing with block length. This notion rests on ensemble arguments over all possible expansions of the base protograph. When…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
This paper considers the construction of isodual quasi-cyclic codes. First we prove that two quasi-cyclic codes are permutation equivalent if and only if their constituent codes are equivalent. This gives conditions on the existence of…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…
We introduce the first example of algebraically constructed hierarchical quasi-cyclic codes. These codes are built from Reed-Solomon codes using a 1964 construction of superimposed codes by Kautz and Singleton. We show both the number of…
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…
In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure…
In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$,…
Quantum synchronizable codes (QSCs) are special quantum error-correcting codes which can be used to correct the effects of quantum noise on qubits and misalignment in block synchronization. In this paper, a new class of quantum…
There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…
This is a manuscript of a chapter prepared for a book. The good codes possess large information length and large minimum distance. A class of codes is said to be asymptotically good if there exists a positive real $\delta$ such that, for…
In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…