Listar por tema "Subfield-subcodes"

New quantum codes from evaluation and matrix-product codes

Galindo, Carlos; Hernando, Fernando; Ruano, Diego Elsevier (2014-07)

Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer ...

On the distance of stabilizer quantum codes from J-affine variety codes

Galindo, Carlos; Geil, Olav; Hernando, Fernando; Ruano, Diego Springer Verlag (2017)

Self-orthogonal J-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but ...

Quantum codes from affine variety codes and their subfield-subcodes

Galindo, Carlos; Hernando, Fernando Springer (2015-07)

We use affine variety codes and their subfield-subcodes to obtain quantum stabilizer codes via the CSS code construction. With this procedure we get codes with good parameters, some of them exceeding the CSS quantum ...

Stabilizer quantum codes from J -affine variety codes and a new Steane-like enlargement

Galindo, Carlos; Hernando, Fernando; Ruano, Diego Springer (2014-09)

New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters [[127,63,≥12]]2 and [[63,45,≥6]]4 that are records. These codes ...

The dimension of subcode-subfields of shortened generalized Reed–Solomon codes

Hernando, Fernando; Marshall, Kyle; O'Sullivan, Michael E. Springer US (2012-03)

Reed–Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where ...