Stabilizer quantum codes defined by trace-depending polynomials |
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Affiliation: | 1. Instituto Universitario de Matemáticas y Aplicaciones de Castellón and Departamento de Matemáticas, Universitat Jaume I, Campus de Riu Sec, 12071 Castelló, Spain;2. Instituto Universitario de Matemáticas y Aplicaciones de Castellón, Universitat Jaume I, Campus de Riu Sec, 12071 Castelló, Spain;3. IMUVA-Mathematics Research Institute, Universidad de Valladolid, 47011 Valladolid, Spain |
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Abstract: | Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace [18]. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a constant plus the trace of a polynomial) and show that this procedure gives rise to stabilizer quantum error-correcting codes with a wider range of lengths than in [18] and with excellent parameters. Namely, we are able to provide new binary records according to [21] and non-binary codes improving the ones available in the literature. |
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Keywords: | Quantum codes Trace Subfield-subcodes Cyclotomic cosets |
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