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On the minimum distance of array codes as LDPC codes

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2 Author(s)
Kyeongcheol Yang ; Dept. of Electron. & Electr. Eng., Pohang Univ. of Sci. & Technol., Kyungbuk, South Korea ; Helleseth, T.

For a prime q and an integer j≤q, the code C(q,j) is a class of low-density parity-check (LDPC) codes from array codes which has a nice algebraic structure. In this correspondence, we investigate the minimum distance d(q,j) of the code in an algebraic way. We first prove that the code is invariant under a doubly transitive group of "affine" permutations. Then, we show that d(5,4)=8, d(7,4)=8, and d(q,4)≥10 for any prime q>7. In addition, we also analyze the codewords of weight 6 in the case of j=3 and the codewords of weight 8 in C(5,4) and C(7,4).

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Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 12 )