一类具有双恢复集的局部恢复码的构造

假设C是有限域Fq上的n,k]线性码,如果码字的每个坐标是其它至多r个坐标的函数,称C是(n,k,r)局部恢复码,这里r是较小的数.在分布式存储系统中,具有多个恢复集的局部恢复码使得数据在系统中更具实际意义,因为它可以避免热数据的频繁访问.引入代数函数域、特别是Hermite函数域去构造局部恢复码,这类局部恢复码具有双恢复集,并且码长可以突破字符集的大小的限制.结果表明,此构造方法得出的最小距离下界明显地改进了Alexander Barg的最小距离的下界.

The Constructions of Locally Recoverable Codes with Double Recovery Sets Over Hermitian Function Fields

Suppose that C is ann,k]linear code over a finite field Fq.If each coordinate of the codeword is a function of up to r other coordinates,then C is an(n,k,r)locally recoverable code,where r is a small number.In distributed storage systems,the locally recoverable codes with multiple recovery sets make data more available in the system,because it can avoid accessing to hot data frequently.In this paper,we introduce algebraic function fields,especially Hermitian function fields,to construct locally recoverable codes.These locally recoverable codes have double recovery sets,and the length of code can break through the limitation of the size of alphabet set.The results show that the lower bound of minimum distance is obtained by this construction method improves the lower bound of Alexander Barg’s minimum distance obviously.