English

Relative generalized Hamming weights of q-ary Reed-Muller codes

Information Theory 2015-11-04 v4 math.IT

Abstract

Coset constructions of qq-ary Reed-Muller codes can be used to store secrets on a distributed storage system in such a way that only parties with access to a large part of the system can obtain information while still allowing for local error-correction. In this paper we determine the relative generalized Hamming weights of these codes which can be translated into a detailed description of the information leakage [2, 24, 21, 11].

Keywords

Cite

@article{arxiv.1407.6185,
  title  = {Relative generalized Hamming weights of q-ary Reed-Muller codes},
  author = {Olav Geil and Stefano Martin},
  journal= {arXiv preprint arXiv:1407.6185},
  year   = {2015}
}

Comments

41 pages. A discussion has been added on how to use secret sharing schemes from q-ary Reed-Muller codes in connection with distributed storage