论文标题
循环和卷积代码与当地
Cyclic and convolutional codes with locality
论文作者
论文摘要
近年来，对本地可回收（LRC）代码及其变体进行了广泛的研究。在本文中，我们着重于LRC代码的循环结构，并在代码的零上得出了支持层次位置属性的代码的条件。结果，我们为新的代码参数获得了层次LRC代码的一般家族。我们还观察到，我们的方法使人们能够以准清晰度形式表示LRC代码，并使用此表示形式构建具有局部性的尾随卷积LRC代码。除其他结果外，我们将具有位置的循环代码扩展到多维环状代码，从而产生具有可用性的LRC代码的新系列，并构建了无限长度的Q-ARY环状层次LRC代码的家族。
Locally recoverable (LRC) codes and their variants have been extensively studied in recent years. In this paper we focus on cyclic constructions of LRC codes and derive conditions on the zeros of the code that support the property of hierarchical locality. As a result, we obtain a general family of hierarchical LRC codes for a new range of code parameters. We also observe that our approach enables one to represent an LRC code in quasicyclic form, and use this representation to construct tail-biting convolutional LRC codes with locality. Among other results, we extend the general approach to cyclic codes with locality to multidimensional cyclic codes, yielding new families of LRC codes with availability, and construct a family of q-ary cyclic hierarchical LRC codes of unbounded length.
