Relative generalized Hamming weights of \(q\)-ary Reed-Muller codes. (English) Zbl 1418.94073
Summary: 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.
MSC:
| 94B05 | Linear codes (general theory) |
| 94A62 | Authentication, digital signatures and secret sharing |
| 94B65 | Bounds on codes |
Keywords:
distributed storage; \(q\)-ary Reed-Muller code; relative generalized Hamming weight; secret sharingReferences:
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