论文标题
翻译不变的度量空间中各种线性度的密度
Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces
论文作者
论文摘要
我们研究具有良好距离特性和规定线性度（包括司额和非线性代码）的误差校正代码的渐近密度。我们专注于有限翻译不变的度量空间的一般设置，然后将结果专门用于锤式度量，并将其置于等级度量标准和总量度量标准。我们的结果表明，代码的渐近密度在很大程度上取决于施加的线性度和所选的度量。
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.
