Quantum codes from Hermitian dual-containing cyclic codes

摘要

A new criterion for the existence of Hermitian dual-containing cyclic codes is obtained based on a characterization of q-cyclotomic cosets modulo n. This criterion admits a method of constructing new Hermitian dual-containing cyclic codes (hence new quantum codes) from the old ones, and enables us to construct several classes of quantum maximum-distance-separable (MDS) codes from classical Hermitian dual-containing cyclic codes. We analyse that our codes are good in certain sense. Besides, some enumerative conclusions are also presented as a result of the characterization of q-cyclotomic cosets modulo n.