1. A memory device with an error detection and correction system formed therein, the error detection and correction system being configured to detect and correct errors in read out data by use of a BCH code, wherein the error detection and correction system is 4-bit error correctable, and searches error locations in such a way as to: divide an error location searching biquadratic equation into two or more factor equations; convert the factor equations to have unknown parts and syndrome parts separated from each other for solving them; and compare indexes of the solution candidates with those of the syndromes, the corresponding relationships being previously obtained as a table, thereby obtaining error locations.