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

In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas

Author

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  • Jon-Lark Kim

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

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.

Suggested Citation

  • Jon-Lark Kim, 2002. "New Quantum Error-Correcting Codes from Hermitian Self-Orthogonal Codes over GF(4)," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 209-213, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_15
    DOI: 10.1007/978-3-642-59435-9_15
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