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

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].

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

References in corpus (3)

• Relative generalized Hamming weights of one-point algebraic geometric codes
• Feng-Rao decoding of primary codes
• On asymptotically good ramp secret sharing schemes

Cited by in corpus (2)

• Higher Hamming weights for locally recoverable codes on algebraic curves
• Relative Generalized Hamming Weights of Cyclic Codes