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In this research paper we discover two different schemes of error detection and correction which are based on parity-check code for optimal error detection and correction utilizing check bits without degrading the data rate too much. The scheme of the first method is obtained by arranging data in rows, to form a square, and then parity bits are added. The second scheme builds upon the first, by forming a square cube and the parity scheme is extended to this shape.

Error Detection and Correction over Two-Dimensional and Two-Diagonal Model and Five-Dimensional Model