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On the Pless-construction and ML decoding of the (48,24,12) quadratic residue code

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3 Author(s)
Esmaeili, M. ; Dept. of Math. Sci., Isfahan Univ. of Technol., Iran ; Gulliver, T.A. ; Khandani, A.K.

We present a method for maximum likelihood decoding of the (48,24,12) quadratic residue code. This method is based on projecting the code onto a subcode with an acyclic Tanner graph, and representing the set of coset leaders by a trellis diagram. This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule. We show that unlike the (24,12,8) Golay code, the (48,24,12) code does not have a Pless-construction which has been an open question in the literature. It is determined that the highest minimum distance of a (48,24) binary code having a Pless (1986) construction is 10, and up to equivalence there are three such codes.

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Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 6 )