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New Optimal Cyclic Locally Recoverable Codes of Length n=2(q+1)
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-01-01 , DOI: 10.1109/tit.2019.2942304
Jianfa Qian , Lina Zhang

Locally recoverable codes are very important due to their applications in distributed storage systems. In this paper, by using cyclic codes, we construct two classes of optimal q-ary cyclic $(\text {r}, \delta _{1})$ locally recoverable codes with parameters $[2(\text {q}+1), 2(\text {q}+1)-2\delta _{1}, \delta _{1}+2]_{\text {q}}$ , where $q$ is an odd prime power and $\text {r}+\delta _{1}-1=\text {q}+1$ , and $(\text {r}, \delta _{2})$ locally recoverable codes with parameters $[2(\text {q}+1), 2(\text {q}+1)-4\delta _{2}+2, \delta _{2}+2]_{q}$ , where $\text {q}\geq 7$ is an odd prime power, $\text {q}\equiv 3~ (mod~ 4)$ and $r+\delta _{2}-1=\frac {\text {q}+1}{2}$ . Compared with the known cyclic and constacyclic $(\text {r}, \delta)$ locally recoverable codes, our construction yields new optimal cyclic $(\text {r}, \delta)$ locally recoverable codes.

中文翻译:

长度为 n=2(q+1) 的新最优循环局部可恢复码

由于其在分布式存储系统中的应用,本地可恢复代码非常重要。在本文中,通过使用循环码,我们构造了两类最优的 q-ary 循环 $(\text {r}, \delta _{1})$ 带参数的本地可恢复代码 $[2(\text {q}+1), 2(\text {q}+1)-2\delta _{1}, \delta _{1}+2]_{\text {q}}$ , 在哪里 $q$ 是一个奇素数幂,并且 $\text {r}+\delta _{1}-1=\text {q}+1$ , 和 $(\text {r}, \delta _{2})$ 带参数的本地可恢复代码 $[2(\text {q}+1), 2(\text {q}+1)-4\delta _{2}+2, \delta _{2}+2]_{q}$ , 在哪里 $\text {q}\geq 7$ 是奇素数幂, $\text {q}\equiv 3~ (mod~ 4)$ $r+\delta _{2}-1=\frac {\text {q}+1}{2}$ . 与已知的循环和恒循环相比 $(\text {r}, \delta)$ 本地可恢复代码,我们的构造产生新的最优循环 $(\text {r}, \delta)$ 本地可恢复代码。
更新日期:2020-01-01
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