代数函数域上快捷恢复LRC码的构造  

Simplified Recovering Method about Locally Recoverable Code on Algebraic Function Field

作　　者：吴珊珊 WU Shanshan(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2021年第3期26-31,共6页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11601009)。

摘　　要：分布式存储系统已经发展到了较大规模,只有引入冗余和编码技术,才能保证系统的稳定性。目前最为先进的编码技术就是局部恢复码(LRC)。将LRC码引入分布式存储系统中,就可以实现较低的恢复成本和较高的恢复效率。利用代数函数域上的三项式构造一类线性LRC码,这类LRC码的恢复过程只要经过一次减法运算。然后,在Hermite函数域上,利用这种快捷恢复的方法,得出当q越大,相对距离越接近最优的LRC码的结论。Distributed storage systems have grown to a larger scale. Only by introducing redundancy and encoding techniques can we guarantee the stability of the system. The most advanced coding technology is the locally recoverable code(LRC). Introducing LRC code into distributed storage system can achieve lower recovery costs and higher recovery efficiency.In this paper, we first construct a class of linear LRC codes using trinomials on algebraic function field, and the recovery process of such LRC codes goes only through one subtraction operation. Then, using this fast recovery method on Hermite function field, we conclude that when q is larger, the relative distance is closer to the optimal LRC code.

关 键 词：局部恢复码 代数函数域 Hermite函数域 

分 类 号：O157.4[理学—数学]