Quantum variations of cyclotomic cosets for cyclic stabiliser codes construction

Cyclotomic cosets are intrinsically linked with the design and construction of classical cyclic codes whose properties can be inferred from the coset structures. This paper proposes some new quantum variations of cyclotomic cosets for cyclic stabiliser construction. These variations are governed by several parameters which are devoted to designing the two essential parts: the error part and the position part of these cosets. Criteria on these cosets in generating additive cyclic stabiliser are extensively studied, followed by actual implementation on stabiliser codes construction of several selected classes of length.