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Structures and Constructions of Subsystem Codes over Finite Fields
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@MISC{Aly_structuresand,
author = {Salah A. Aly},
title = {Structures and Constructions of Subsystem Codes over Finite Fields},
year = {}
}
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Abstract
Abstract—Quantum information processing is a rapidly mounting field that promises to accelerate the speed up of computations. The field utilizes the novel fundamental rules of quantum mechanics such as accelerations. Quantum states carrying quantum information are tempted to noise and decoherence, that’s why the field of quantum error control comes. In this paper, we investigate various aspects of the general theory of quantum error control- subsystem codes. Particularly, we first establish two generic methods to derive subsystem codes from classical codes that are defined over finite fields Fq and F q 2. Second, we derive cyclic subsystem codes and using our two methods, we derive all classes of subsystem codes. Consequently, we construct two famous families of cyclic subsystem BCH and RS codes. Cyclic subsystem RS codes are turned out to be Optimal and MDS codes saturating the singleton bound with equality. Third, we demonstrate several methods of subsystem code constructions by extending, shortening and combining given subsystem codes. Finally, we present tables of upper and lower bounds on subsystem codes parameters 1. I.
Keyphrases
subsystem code finite field generic method general theory quantum information cyclic subsystem bch quantum error control famous family various aspect present table md code singleton bound quantum mechanic r code finite field fq classical code quantum error control subsystem code subsystem code parameter cyclic subsystem code subsystem code construction abstract quantum information processing novel fundamental rule several method cyclic subsystem r code
