代数函数域上的局部恢复码

Locally recoverable codes on the algebraic function fields

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)线性码,这里r是较小的数.本文在代数函数域上构造出了局部恢复码,它的码长不受字符集大小的限制,实际上,它的码长可以远远大于字符集的大小;并将此方法应用于广义Hermite函数域,得到了一类广义Hermite函数域上的局部恢复码.进一步地,通过构造子码的方式改进了广义Hermite函数域上的局部恢复码的最小距离的下界.

Suppose that C is the[n,k]linear code on the finite field Fq.If each coordinate of the codeword is a function of other up to r coordinates,we call that C is the(n,k,r)locally recoverable code,here r is the smaller number.In this paper,a locally recoverable code is constructed on the algebraic function field.The length of the code is not limited by the alphabet set,that is,the length of the code can be much larger than the size of the alphabet set.The construction method is applied to the generalized Hermitian function field.A class of locally recoverable code on the generalized Hermitian functions is obtained.Further,the lower bound of the minimum distance of the locally recoverable code on the generalized Hermitian function field is improved by constructing the subcode.