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A general algorithm for decoding the binary systematic quadratic residue (QR) codes with lookup tables is presented in this study. The algorithm can be applied in decoding the QR codes with either reducible or irreducible generator polynomials. If the generator polynomial of the QR codes is reducible, the number of elements in the Galois field is less than the sum of all correctable error patterns...
The key ideas behind this decoding technique are utilizing the shift search algorithm. Only those error patterns of weight less than 5 are necessary to be stored in the memory. By utilizing the hash search scheme for finding error pattern, the decrease of CPU time in decoding process is about 38% and the size of memory requirement is about 6% more than binary search scheme. Moreover, the new method...
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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