For a Distributed Storage System (DSS), the Fractional Repetition (FR) code is a class in which replicas of encoded data packets are stored on distributed chunk servers, where the encoding is done using the Maximum Distance Separable (MDS) code. The FR codes allow for the exact uncoded repair with minimum repair bandwidth. In this paper, FR codes (called Flower codes) are constructed using finite binary sequences. It is shown that, for any FR code, there exists a Flower code and therefore Flower code is the general framework to construct FR code with uniform as well as non-uniform parameters. The condition for universally good Flower code is calculated on such sequences. For some sequences, the universally good Flower codes and Locally Repairable Flower codes are explored. In addition, conditions for equivalent Flower codes and dual Flower codes are also investigated in this paper. Some families of Flower codes with non-uniform parameters are obtained such that, from those families, Flowers code with uniform parameters are optimal FR codes in the literature. It is shown that any FR code is a Flower code and some known FR codes are obtained as the special cases of Flower codes using sequences.

中文翻译：

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关于不均匀的花代码

对于分布式存储系统（DSS），小数重复（FR）代码是一类，其中已编码数据包的副本存储在分布式块服务器上，其中使用最大距离可分离（MDS）代码进行编码。FR代码允许以最小的维修带宽进行精确的未编码维修。在本文中，FR码（称为花码）是使用有限的二进制序列构造的。结果表明，对于任何FR代码，都存在Flower代码，因此Flower代码是构造具有统一和非统一参数的FR代码的通用框架。在这样的序列上计算出普遍适用的花朵代码的条件。对于某些序列，探索了普遍适用的花朵代码和本地可修复花朵代码。此外，本文还研究了等效的花代码和双重花代码的条件。获得了具有不一致参数的Flower代码的某些族，从而从这些族中，具有一致参数的Flower代码是文献中的最佳FR代码。可以看出，任何FR码都是Flower码，并且使用序列获得了一些已知的FR码作为Flower码的特例。