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Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. They generalize all major quantum error protection schemes, and therefore are especially versatile. This paper introduces numerous constructions of subsystem codes. It is shown how one can derive subsystem codes from classical cyclic codes. Methods to trade the dimensions of subsystem and co-subsystem are introduced that maintain or improve the minimum distance. As a consequence, many optimal subsystem codes are obtained. Furthermore, it is shown how given subsystem codes can be extended, shortened, or combined to yield new subsystem codes. These subsystem code constructions are used to derive tables of upper and lower bounds on the subsystem code parameters. [ABSTRACT FROM AUTHOR]

Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes. But for given restricted length n, good quantum BCH codes are very sparse. In this paper, by puncturing and pasting check matrices of Hermitian dual containing BCH codes over the quaternary field, we construct many linear quantum codes with good parameters, and some of them have parameters exceeding the finite Gilbert-Varshamov bound for stabilizer quantum codes. [ABSTRACT FROM AUTHOR]

Quasi-cyclic codes form a generalization of cyclic codes, and contain a large number of record breaking codes. In this paper, we provide a method for constructing self-orthogonal quasi-cyclic codes, and obtain a large number of new quantum quasi-cyclic codes by CSS construction. [ABSTRACT FROM AUTHOR]