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A modified algebraic decoding algorithm (ADA) is presented to decode up to five possible errors in a binary systematic (47, 24, 11) quadratic residue (QR) code. The main key points of the proposed ADA are to modify the erroneous conditions in Case 3, Case 4, and Case 5 of the ADA given in He et al. (2001) and to find out the true conditions from Case 2 to Case 5. The new conditions can also be applied...
Recently, a novel decoding procedure which is called the syndrome-weight determination for the Golay code, or the (23, 12, 7) quadratic residue code, was proposed by Chang et al. This method is not only very simple in principle but also suitable for the parallel hardware design. Furthermore, to develop a universal decoding algorithm for arbitrary binary quadratic residue codes is very important. In...
An efficient and fast decoding algorithm, called the syndrome-weight decoding algorithm (SWDA), is proposed to decode three possible errors for the binary systematic (23, 12, 7) quadratic residue (QR) code. The proposed SWDA uses the properties of weight of syndrome to decode this QR code. Simulation results show that the SWDA is highly efficient. The SWDA is also compared with other known decoding...
A new effective lookup table for decoding the binary systematic (41, 21, 9) quadratic residue (QR) code up to 4 errors is presented in this paper. The key ideas behind this decoding technique are based on one to one mapping between the syndromes ldquoS1rdquo and the error correctable patterns. Such an algorithm determines the error locations directly by lookup tables without the operations of multiplication...
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