Related papers: An infinite class of quantum codes derived from du…
We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived…
In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum…
We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…
In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
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…
Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand,…
Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…
Self-orthogonal $J$-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the…
One hurdle to performing reliable quantum computations is overcoming noise. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers.…
This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over Fq2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given…
In this paper, we construct several infinite families of $q$-ary constacyclic codes over a finite field $\mathbb{F}_q$ with length $n$, dimension around $n/2$, and minimum distance at least $cn/\log_q n$ for some positive constant $c$. They…
We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They…
Entanglement-assisted quantum error correcting codes (EAQECCs) can be derived from arbitrary classical linear codes. However, it is a very difficult task to determine the number of entangled states required. In this work, using the method…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code.…
Constacyclic codes over finite fields are of theoretical importance as they are closely related to a number of areas of mathematics such as algebra, algebraic geometry, graph theory, combinatorial designs and number theory. However, the…
Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…