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

Olav Geil; Stefano Martin

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arXiv · 1407.6185

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

Olav Geil·Stefano Martin

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Abstract

Coset constructions of $q$-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].

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Olav Geil, Stefano Martin. 2015-11-03. Relative generalized Hamming weights of q-ary Reed-Muller codes. https://arxiv.org/abs/1407.6185

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