We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on the general setting of finite translation-invariant metric spaces, and then specialize our results to the Hamming metric, to the rank metric, and to the sum-rank metric. Our results show that the asymptotic density of codes heavily depends on the imposed linearity degree and the chosen metric.

翻译：我们调查误差校正代码的无症状密度,该代码具有良好的距离属性和规定的直线度,包括亚线性和非线性代码。我们侧重于有限翻译差异度空间的一般设置,然后将结果专门用于哈明度、等级度度和总级度。 我们的结果表明,代码的无症状密度在很大程度上取决于强制的直线度和选择的度量。