Construction of all-symbol locally repairable codes with unequal availability

Abstract:

The existing all-symbol locally repairable codes with unequal availability have limited parameter values, and low code rates. In order to solve the problems above, this paper constructs a class of all-symbol locally repairable codes with unequal availability based on saturated orthogonal arrays, which achieves higher code rates. Specifically, the association matrix is generated based on the saturated orthogonal array, and the matrix transformations as well as the Kronecker product operations are performed on the association matrix to generate all-symbol locally repairable codes with high availability of information symbols and unequal availability of information bits. Theoretical analyses show that all-symbol locally repairable codes with high availability of information symbols have flexible parameter values and are optimal in dimension and code length at locality r=2. Compared with the existing all-symbol locally repairable codes, the constructed all-symbol locally repairable codes with unequal availability of information bits perform better in terms of code rate.