English

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

Information Theory 2019-03-20 v1 math.IT

Abstract

The weight distribution of second order qq-ary Reed-Muller codes have been determined by Sloane and Berlekamp (IEEE Trans. Inform. Theory, vol. IT-16, 1970) for q=2q=2 and by McEliece (JPL Space Programs Summary, vol. 3, 1969) for general prime power qq. 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 qq-ary Reed-Muller codes. In addition, the weight distributions of second order qq-ary homogeneous Reed-Muller codes and second order qq-ary projective Reed-Muller codes are also determined.

Keywords

Cite

@article{arxiv.1903.08058,
  title  = {On the weight distribution of second order Reed-Muller codes and their relatives},
  author = {Shuxing Li},
  journal= {arXiv preprint arXiv:1903.08058},
  year   = {2019}
}

Comments

14 pages, Designs, Codes and Cryptography, Accepted, 2019