New Quantum Error-Correcting Codes from Hermitian Self-Orthogonal Codes over GF(4)

Jon-Lark Kim
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Jon-Lark Kim: University of Illinois-Chicago, Department of Mathematics, Statistics, and Computer Science, 322 SEO(M/C 249)

A chapter in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, 2002, pp 209-213 from Springer

Abstract: Abstract In order to construct good quantum-error-correcting codes, we construct good Hermitian self-orthogonal linear codes over GF(4). In this paper we construct record-breaking pure quantum-error-correcting codes of length 24 with 2 encoded qubits and minimum weight 7 from Hermitian self-orthogonal codes of length 24 with dimension 11 over GF(4). This shows that length n = 24 is the smallest length for any known [[n, k, d]] quantum-error-correcting code with k ≥ 2 and d = 7. We also give a construction method to produce Hermitian self-orthogonal linear codes GF(4) from a shorter length such code.

Keywords: Linear Code; Minimum Weight; Cyclic Code; Association Scheme; Quantum Code (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59435-9_15

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DOI: 10.1007/978-3-642-59435-9_15

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