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On efficient majority logic decodable codes

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A particular shortening technique is applied to majority logic decodable codes of length2^{t}. The shortening technique yields new efficient codes of lengthsn = 2^{p}, wherepis a prime, e.g., a (128,70) code withd_{maj} = 16. For moderately long code lengths (e.g.,n = 2^{11} or 2^{13}), a 20-25 percent increase in efficiency can be achieved over the best previously known majority logic decodable codes. The new technique also yields some efficient codes for lengthsn = 2^{m}wheremis a composite number, for example, a (512,316) code withd_{maj} = 32code which has 42 more information bits than the previously most efficient majority logic decodable code.

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Information Theory, IEEE Transactions on  (Volume:22 ,  Issue: 6 )