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New covering radius of Reed-Muller codes for \(t\)-resilient functions. (English) Zbl 1288.94067
The authors introduce a new covering radius of \(\text{RM}(r,n)\) from the cryptography viewpoint that is defined as the maximum distance between \(t\)-resilient functions and the \(r\)th order Reed-Muller code \(\text{RM}(r,n)\). They give its lower and upper bounds and present a table of numerical data of their bounds.

MSC:
94A60 Cryptography
94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory
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