<p><it>Abstract—</it>In the literature, $<tmath>m_{j}</tmath>$-projection has been applied for residue error detection and correction. This brief contribution extends the $<tmath>m_{j}</tmath>$-projection to $<tmath>k</tmath>$-term $<tmath>m_{j}</tmath>$-projection so that single residue error correction can be accomplished in an efficient manner. Based on $<tmath>k</tmath>$-term $<tmath>m_{j}</tmath>$-projection, the necessary and sufficient conditions for the correction of single residue digit error are derived and an efficient procedure for single error correction is given.</p><p><it>Index Terms—</it>Error detection and correction, residue number systems, residue arithmetic.</p>