Stabilizer quantum codes defined by trace-depending polynomials
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929556874592256 |
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| author | Galindo, Carlos Hernando, Fernando Martín-Cruz, Helena Ruano, Diego |
| author_facet | Galindo, Carlos Hernando, Fernando Martín-Cruz, Helena Ruano, Diego |
| contents | Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. 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 other papers involving roots of the trace and with excellent parameters. Namely, we are able to provide new binary records and non-binary codes improving the ones available in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_06187 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stabilizer quantum codes defined by trace-depending polynomials Galindo, Carlos Hernando, Fernando Martín-Cruz, Helena Ruano, Diego Information Theory Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. 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 other papers involving roots of the trace and with excellent parameters. Namely, we are able to provide new binary records and non-binary codes improving the ones available in the literature. |
| title | Stabilizer quantum codes defined by trace-depending polynomials |
| topic | Information Theory |
| url | https://arxiv.org/abs/2208.06187 |