In this article we improve the dimension and minimum distance bound of the the Hermitian Lifted Codes LRCs construction from L\'opez, Malmskog, Matthews, Pi\~nero and Wooters via elementary univariarte polynomial division. They gave an asymptotic rate estimate of $0.007$. We improve the rate estimate to $0.1$ using univariate polynomial division
翻译:本文通过初等单变量多项式除法改进了López、Malmskog、Matthews、Piñero和Wooters所构造的Hermitian Lifted Codes局部可修复码的维数与最小距离界。该构造原先给出的渐近速率估计为$0.007$,我们利用单变量多项式除法将速率估计提升至$0.1$。