Relative generalized Hamming weights of q-ary Reed-Muller codes
Information Theory
2015-11-04 v4 math.IT
Abstract
Coset constructions of -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