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On quasi-cyclic codes with rate l m (Corresp.)

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1 Author(s)

An integer linear programming problem and an additional divisibility condition are described such that they have a common solution if and only if there is a quasi-cyclic code with rate 1/m . A table of binary quasi-cyclic codes with dimensions seven and eight and rate 1/m for small m is included. In particular, there are binary linear codes with (length, dimension, minimum distance) =(35, 7,16), (42, 7,19), (80, 8, 37), (96, 8, 46) , and (112,8,54) .

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Information Theory, IEEE Transactions on  (Volume:24 ,  Issue: 5 )