In classical coding theory, it is common to construct new codes via propagation rules. There are various propagation rules to construct classical block codes. However, propagation rules have not been extensively explored for constructions of locally repairable codes. In this paper, we introduce a few propagation rules to construct good locally repairable codes. To our surprise, these simple propagation rules produce a few interesting results. Firstly, by concatenating a locally repairable code as an inner code with a classical block code as an outer code, we obtain quite a few dimension-optimal binary locally repairable codes. Secondly, from this concatenation, we explicitly build a family of locally repairable codes that exceeds the Zyablov-type bound. Thirdly, by a lengthening propagation rule that adds some rows and columns from a parity-check matrix of a given linear code, we are able to produce a family of dimension-optimal binary locally repairable codes from the extended Hamming codes, and to convert a classical maximum distance separable (MDS) code into a Singleton-optimal locally repairable code. Furthermore, via the lengthening propagation rule, we greatly simplify the construction of a family of locally repairable codes in \cite[Theorem 5]{MX20} that breaks the asymptotic Gilbert-Varshamov bound. In addition, we make use of three other propagation rules to produce more dimension-optimal binary locally repairable codes. Finally, one of phenomena that we observe in this paper is that some trivial propagation rules in classical block codes do not hold anymore for locally repairable codes.

翻译：在古典编码理论中,通过传播规则构建新的代码是常见的。有各种传播规则来构建古典区块代码。 但是, 尚未对本地可修理代码的构建进行广泛探讨。 在本文中, 我们引入了一些传播规则来构建良好的本地可修理代码。 令我们惊讶的是, 这些简单的传播规则产生了一些有趣的结果。 首先, 通过将本地可修理代码混成一个内部代码, 以经典区块代码作为外源代码, 我们获得了一个相当多的尺寸最佳的本地可修理代码。 其次, 从这种交配中, 我们明确建立了一套本地可修理代码, 超过了Zyablov 型的装订。 第三, 通过延长的传播规则, 将某些行和列从某特定线性代码的对等检查矩阵中添加一些行和列, 我们能够生成一个内装最优的本地可修理代码, 并且将一个可复制的最大距离( MDS) (MDS) 代码转换成一个单质- 本地可修理代码。 此外, 我们通过超长的版本版本版本版本规则, 将本地的版本规则 将本地的版本的版本改成另一个的版本的版本的版本规则 。