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This paper presents a construction algorithm for the short block irregular LDPC codes. By applying a magic square theorem as a part of the matrix construction, a newly developed algorithm, the so-called Magic Square Based Algorithm (MSBA), is obtained. The modified array codes are focused on in this study since the reduction of 1s can lead to simple encoding and decoding schemes. Simulation results based on AWGN channels show that with the code rate of 0.8 and SNR = 5 dB, the BER of 10-7 can be obtained whilst the number of decoding iteration is relatively low.