Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes

@article{Carlet2007ImprovingTU,
  title={Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes},
  author={Claude Carlet and Sihem Mesnager},
  journal={IEEE Transactions on Information Theory},
  year={2007},
  volume={53},
  pages={162-173}
}
By deriving bounds on character sums of Boolean functions and by using the characterizations, due to Kasami , of those elements of the Reed-Muller codes whose Hamming weights are smaller than twice and a half the minimum distance, we derive an improved upper bound on the covering radius of the Reed-Muller code of order 2, and we deduce improved upper bounds on the covering radii of the Reed-Muller codes of higher orders 

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