Correction of $2$-Dimensional Occasional and Cluster Errors in $LRTJ$-Spaces

Abstract

Two-dimensional codes in $LRTJ$ spaces are subspaces of the space $Ma{t}_{m\times s}({\mathbb{Z}}_q)$, 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.