Quantum Error Correction via Codes over GF(2)

Chowdhury, Arijit and Rajan, Sundar B (2009) Quantum Error Correction via Codes over GF(2). In: IEEE International Symposium on Information Theory (ISIT 2009), JUN 28-JUL 03, 2009, Seoul, pp. 789-793.

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Abstract

It is well known that n-length stabilizer quantum error correcting codes (QECCs) can be obtained via n-length classical error correction codes (CECCs) over GF(4), that are additive and self-orthogonal with respect to the trace Hermitian inner product. But, most of the CECCs have been studied with respect to the Euclidean inner product. In this paper, it is shown that n-length stabilizer QECCs can be constructed via 371 length linear CECCs over GF(2) that are self-orthogonal with respect to the Euclidean inner product. This facilitates usage of the widely studied self-orthogonal CECCs to construct stabilizer QECCs. Moreover, classical, binary, self-orthogonal cyclic codes have been used to obtain stabilizer QECCs with guaranteed quantum error correcting capability. This is facilitated by the fact that (i) self-orthogonal, binary cyclic codes are easily identified using transform approach and (ii) for such codes lower bounds on the minimum Hamming distance are known. Several explicit codes are constructed including two pure MDS QECCs.

Item Type:	Conference Paper
Publisher:	IEEE
Additional Information:	Copyright 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	23 Aug 2010 13:00
Last Modified:	19 Sep 2010 06:14
URI:	http://eprints.iisc.ac.in/id/eprint/31346

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