On the weight distribution of second order Reed-Muller codes and their relatives

03/19/2019

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by   Shuxing Li, et al.

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Otto-von-Guericke-University Magdeburg

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The weight distribution of second order q-ary Reed-Muller codes have been determined by Sloane and Berlekamp (IEEE Trans. Inform. Theory, vol. IT-16, 1970) for q=2 and by McEliece (JPL Space Programs Summary, vol. 3, 1969) for general prime power q. Unfortunately, there were some mistakes in the computation of the latter one. This paper aims to provide a precise account for the weight distribution of second order q-ary Reed-Muller codes. In addition, the weight distributions of second order q-ary homogeneous Reed-Muller codes and second order q-ary projective Reed-Muller codes are also determined.