Correction of \(2\)-Dimensional Occasional and Cluster Errors in \(LRTJ\)-Spaces

Abstract

Two-dimensional codes in \(LRTJ\) spaces are subspaces of the space \(Mat_{m\times s}(\mathbb{Z}_q)\), the linear space of all \(m \times s\)-matrices with entries from a finite ring \(\mathbb{Z}_q\), endowed with the \(LRTJ\)-metric \([3,9]\). Also, the error-correcting capability of a linear code depends upon the number of parity-check symbols. In this paper, we obtain a lower bound on the number of parity checks of two-dimensional codes in \(LRTJ\)-spaces correcting both independent as well as cluster array errors.