A locally repairable code (LRC) with locality r allows for the recovery of any erased symbol of a codeword by accessing only r other symbols of the same codeword. The LRCs achieving the Singleton-like bound are said to be optimal. In this paper, we completely characterize the locality of any constacyclic codes of length ps over finite fields. Using this characterization, we determine all the optimal constacyclic LRCs of prime power lengths over finite fields, i.e., there are no other optimal constacyclic LRCs of prime power length except for those we characterized in this paper. We classify all the optimal constacyclic LRCs into seven classes. The first six classes of constacyclic LRCs classified in this paper have unbounded length, and can achieve smaller locality comparing to those codes constructed by Luo, Xing and Yuan, which also provide unbounded length.
展开▼
机译:局部性为r的本地可修复代码(LRC)允许通过仅访问r个相同码字的其他符号来恢复该码字的任何已擦除符号。据说达到单例样边界的LRC是最优的。在本文中,我们完全刻画了长度为p的任何并发码的局部性
s sup>
在有限的领域。利用这种特征,我们确定了有限域上所有本征功率长度的最优恒循环LRC,即除了本文中所描述的那些以外,没有其他本征功率长度的最优恒循环LRC。我们将所有最佳恒定循环LRC分为七个类别。本文分类的前六类恒定周期LRC具有无限制的长度,并且与由Luo,Xing和Yuan构造的代码(也提供无限制的长度)相比,可以实现较小的局部性。
展开▼