Symplectically self-orthogonal additive codes and their applications to quantum stabilizer codes

Steven Dougherty T., Kashyap N., Sidana T., Şahinkaya S., Ustun D.

Conference NonCommutative Rings and their Applications, 2023 and Conference Quadratic Forms, Rings and Codes, 2023, Hybrid, Lens, Fransa, 31 Ağustos 2023, cilt.826, ss.87-101, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 826
  • Doi Numarası: 10.1090/conm/826/16574
  • Basıldığı Şehir: Hybrid, Lens
  • Basıldığı Ülke: Fransa
  • Sayfa Sayıları: ss.87-101
  • Anahtar Kelimeler: Additive codes, quantum codes, self-orthogonal codes
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, for a given duality M of the additive group of a finite commutative Frobenius ring R, we define an M-symplectic inner-product on R2n. For any pair of dualities M and M′ of R, we show that an M-symplectically self-orthogonal additive code is symplectically isometric to a M′-symplectically self-orthogonal additive code. As a consequence, we observe that for a given duality M of R, M-symplectically self-orthogonal additive codes over R give rise to the construction of quantum stabilizer codes. Given this relationship, we then describe constructions for self-orthogonal additive codes over a ring R with any duality.