arXiv subjects

Salah A. Aly

Publications and source records attributed to Salah A. Aly.

56 records · Page 4Linked to original sources

arXiv2006

On Quantum and Classical BCH Codes

Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its dual code only if its designed distance d=O(sqrt(n)), and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and - consequently - the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters.

quant-ph↗

arXiv2006

Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes

Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand, do not require active error correction, but perform poorly in terms of minimum distance. In this paper, examples of degenerate quantum codes are constructed that have better minimum distance than decoherence free subspaces and allow some errors of small weight that do not require active error correction. In particular, two new families of [[n,1,>= sqrt(n)]]_q degenerate quantum codes are derived from classical duadic codes.

quant-ph↗