Journal ArticleDOI
On quantum codes via cyclic codes of arbitrary length over 𝔽4 + u𝔽4
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In this paper, a necessary and sufficient condition for a cyclic code over R to contain its dual is determined, and the odd and even length cases are discussed in both cases.Abstract:
In this paper, we study cyclic codes over R=𝔽4+u𝔽4,u2 = 0. A necessary and sufficient condition for a cyclic code over R to contain its dual is determined. The odd and even length cases are discuss...read more
Citations
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Journal ArticleDOI
New Quantum and LCD Codes Over the Finite Field of Odd Characteristic
TL;DR: This paper finds new and better quantum error-correcting codes than previously known quantum error correcting codes over a finite non-chain ring and characterize the LCD codes and obtain many new LCD codes.
Journal ArticleDOI
On quantum and LCD Codes Over The Ring Fq+vFq+v2Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_q+vF_q+v^2F_q$$\en
TL;DR: The aim of this paper is to study cyclic codes over a non-chain ring R = Fq + v F q + v 2 F q, where v 3 = v and better quantum error-correcting codes are described.
References
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A single quantum cannot be cloned
TL;DR: In this article, the linearity of quantum mechanics has been shown to prevent the replication of a photon of definite polarization in the presence of an excited atom, and the authors show that this conclusion holds for all quantum systems.
Journal ArticleDOI
Scheme for reducing decoherence in quantum computer memory
TL;DR: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits\char22{}techniques that may become the key to practical quantum computing on a large scale.
Journal ArticleDOI
Quantum error correction via codes over GF(4)
TL;DR: In this article, the problem of finding quantum error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a trace inner product.
Journal ArticleDOI
Enlargement of Calderbank-Shor-Steane quantum codes
TL;DR: It is shown that a classical error correcting code C, which contains its dual, C/sup /spl perp///spl sube/C, and which can be enlarged to C'=[n,k'>k+1,d'], can be converted into a quantum code of parameters [[ n,k+k'-n,min(d,[3d'/2])]].
Journal ArticleDOI
Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2
Taher Abualrub,Irfan Siap +1 more
TL;DR: The rank, the dual, and the Hamming distance of these codes are studied as well as examples of cyclic codes of various lengths.