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A Lower Bound on the Optimum Distance Profiles of the Second-Order Reed–Muller Codes

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2 Author(s)
Yanling Chen ; Fraunhofer IESE, Kaiserslautern, Germany ; Vinck, A.J.H.

In this paper, we give a lower bound for the optimum distance profiles of the second-order Reed-Muller code in the dictionary order and in the inverse dictionary order. In particular, we investigate the second-order Reed-Muller codes of length ≤ 256. We show that the bound is tight in both orders for the codes of length ≤ 128 .

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Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 9 )