New quantum codes from evaluation and matrix-product codes
Institution:
1. Instituto Universitario de Matemáticas y Aplicaciones de Castellón, and Departamento de Matemáticas, Universitat Jaume I, Campus de Riu Sec., 12071 Castelló, Spain;2. Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, Denmark
Abstract:
Stabilizer codes obtained via the CSS code construction and the Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed–Muller, hyperbolic and affine variety codes are studied. Stabilizer codes with good quantum parameters are supplied; in particular, some binary codes of lengths 127 and 128 improve the parameters of the codes in http://www.codetables.de. Moreover, non-binary codes are presented either with parameters better than or equal to the quantum codes obtained from BCH codes by La Guardia or with lengths that cannot be reached by them.
