论文标题
通过子空间多项式修复芦苇 - 固体代码
Repairing Reed-Solomon Codes via Subspace Polynomials
论文作者
论文摘要
我们提出了用于使用子空间多项式的芦苇 - 固体代码的新修复方案，因此在使用痕量多项式的文献中推广了先前的作品。芦苇 - 溶剂代码超过$ \ mathbb {f} _ {q^\ ell} $，并具有冗余$ r = n-k \ geq q^m $，$ 1 \ leq m \ leq \ ell $，其中$ n $和$ k $是代码长度和尺寸。特别是，对于一次擦除，我们表明我们的方案可以在$ n = q^\ ell $和$ r = q^m，$ for ahl $ 1 \ leq m \ leq \ ell $时，就可以实现最佳维修带宽。对于两种擦除，我们的计划使用每次擦除的带宽与单个擦除计划相同的带宽，对于$ \ ell/m $，使用$ q $的功率为$ Q $，而$ \ ell = q^a $，$ m = q^b-1> 1 $（$ a \ a \ geq b \ geq b \ geq 1 $），对于$ m \ geq e el $ el/2 $ y是$ el/2 $，又是$ el/2 $。
We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature that employ trace polynomials. The Reed-Solomon codes are over $\mathbb{F}_{q^\ell}$ and have redundancy $r = n-k \geq q^m$, $1\leq m\leq \ell$, where $n$ and $k$ are the code length and dimension, respectively. In particular, for one erasure, we show that our schemes can achieve optimal repair bandwidths whenever $n=q^\ell$ and $r = q^m,$ for all $1 \leq m \leq \ell$. For two erasures, our schemes use the same bandwidth per erasure as the single erasure schemes, for $\ell/m$ is a power of $q$, and for $\ell=q^a$, $m=q^b-1>1$ ($a \geq b \geq 1$), and for $m\geq \ell/2$ when $\ell$ is even and $q$ is a power of two.
