Barbero-Lucas Beatriz, Hernando Fernando, Martín-Cruz Helena, McGuire Gary
School of Mathematics and Statistics, University College Dublin, Dublin, Ireland.
Instituto Universitario de Matemáticas y Aplicaciones de Castellón and Departamento de Matemáticas, Universitat Jaume I, Campus de Riu Sec, 12071 Castelló, Spain.
Quantum Inf Process. 2024;23(3):86. doi: 10.1007/s11128-024-04297-x. Epub 2024 Mar 1.
We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. Generalized monomial-Cartesian codes arise from polynomials in variables. When our codes are MDS, and when and our lower bound for the minimum distance is 3, the codes are at least Hermitian almost MDS. For an infinite family of parameters, when we prove that our codes beat the Gilbert-Varshamov bound. We also present many examples of our codes that are better than any known code in the literature.
我们从广义单项式 - 笛卡尔码构造新的稳定子量子纠错码。我们的构造使用了一个明确定义的扭转向量，并给出了最小距离和维度的公式。广义单项式 - 笛卡尔码源自多变量多项式。当我们的码是MDS码时，以及当 且我们的最小距离下界为3时，这些码至少是厄米特几乎MDS码。对于一个无穷参数族，当 时，我们证明我们的码优于吉尔伯特 - 瓦尔沙莫夫界。我们还给出了许多我们的码的例子，它们比文献中任何已知的码都要好。
