Related papers: On the Construction of Optimal Asymmetric Quantum …
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic…
Sarvepalli and Klappenecker showed how classical one-point codes on the Hermitian curve can be used to construct quantum codes. Homma and Kim determined the parameters of a larger family of codes, the two-point codes. In quantum…
A family of $\omega$-circulant balanced weighing matrices with classical parameters is used for the construction of optimal constant weight codes over an alphabet of size $g+1$ and length $n=(q^m -1)/(q-1)$, where $q$ is an odd prime power,…
This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…
Classes of self-dual codes and dual-containing codes are constructed. The codes are obtained within group rings and, using an isomorphism between group rings and matrices, equivalent codes are obtained in matrix form. Distances and other…
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…
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…
In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…
One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
In this paper, we shall give an explicit proof that constacyclic codes over finite commutative rings can be realized as ideals in some twisted group rings. Also, we shall study isometries between those codes and, finally, we shall study…
Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional…
A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo $2^{m}$ is a linear code with property that if the codeword $(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift $(c_1,c_2,...,c_0)\in \mathcal{C}$.…
Quantum error correcting codes (QECC) is becoming an increasingly important branch of coding theory. For classical block codes, a \href{codetables.de} {comprehensive database of best known codes} exists which is available online at…
In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of…
Recently, the theory of quantum error control codes has been extended to subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in…
For $(n,d)= (66,17),(78,19)$ and $(94,21)$, we construct quantum $[[n,0,d]]$ codes which improve the previously known lower bounds on the largest minimum weights among quantum codes with these parameters. These codes are constructed from…