Algebraic decoding of the (23,12,7) Golay code
IEEE Transactions on Information Theory
Some decomposable codes: the |a+x|b+x|a+b+x| construction
IEEE Transactions on Information Theory
Even more efficient bounded-distance decoding of the hexacode, the Golay code, and the Leech lattice
IEEE Transactions on Information Theory
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We consider linear composite codes based on the |a+x|b+x|a+b+x| construction. For m ≥ 3 and r ≤ 4m + 3, we propose a class of linear composite [3 · 2m, 3 · 2m − r, 8] codes, which includes the [24,12,8] extended Golay code. We describe an algebraic decoding algorithm, which is valid for any odd m, and a simplified version of this algorithm, which can be applied for decoding the Golay code. We give an estimate for the combinational-circuit decoding complexity of the Golay code. We show that, along with correction of triple independent errors, composite codes with minimum distance 8 can also correct single cyclic error bursts and two-dimensional error bytes.