Operator MDS Quantum Error Correcting Codes of Lenght (q^2-1)/λ

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Sarı M.

4th International Congress on Multidisciplinary Natural Sciences and Engineering, Ankara, Türkiye, 7 - 08 Aralık 2024, ss.319-326

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Ankara
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.319-326
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

One of the significant families of quantum error correction codes is the operator quantum error correcting codes which arised from the notion of encoding a quantum information into a subsystem of Hilbert space instead of a subspace of Hilbert space. This is the reason why operator quantum error correcting codes are also called as subsystem codes. There have been enormous studies on constructing operator maximum distance separable error correcting codes. An operator quantum error correcting code is called maximum distance separable (MDS) if its parameters attain the Singleton bound for operator quantum error correcting codes. Let  be an odd prime power and  be an odd divisor of  greater than . In this study, by making use of constacyclic codes of length  over finite fields of  elements, we aim to construct a class of operator maximum distance separable (MDS) quantum error correcting codes of length  . We define their defining sets such that corresponding constacyclic codes are maximum distance separable and contain their duals with respect to Hermitian inner products. Via Hermitian construction for operator quantum error correction codes, we get a class of operator maximum distance separable quantum error correcting codes of length . Finally, we tabulate our parameters and show that they include the existing ones in literature.