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The Covering Radius of the Reed-Muller Code R(3, 7) in R(5, 7) Is 20
Gui LI Qichun WANG Shi SHU
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2019/03/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Coding Theory
covering radius, Reed-Muller codes, third-order nonlinearity, Boolean function,
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We propose a recursive algorithm to reduce the computational complexity of the r-order nonlinearity of n-variable Boolean functions. Applying the algorithm and using the sufficient and necessary condition put forward by  to cut the vast majority of useless search branches, we show that the covering radius of the Reed-Muller Code R(3, 7) in R(5, 7) is 20.