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