9th International IFS and Contemporary Mathematics and Engineering Conference, Mersin, Turkey, 8 - 11 July 2023, pp.15
An
(n,
k, r) locally
recoverable code (for shortly LRC) is a code of length n and dimension k over a finite field such that a symbol
in any coordinate of a codeword can be recovered by accessing the symbols in at
most r
other coordinates.
These codes are used in distributed storage systems by Microsoft Azure and Hadoop
since they can recover a failed node by accessing the minimum number of the surviving
nodes. A matrix is called as an (r, t)-regular matrix if its each row has uniform weight r and each column has uniform weight t. In this study, new (r, t)-regular matrices are obtained by using
the magic squares and the parametrization of an LRC code is given by using these
(r, t)-regular matrices.