The Covering Radius of the Reed-Muller Code R(3, 7) in R(5, 7) Is 20

Gui LI  Qichun WANG  Shi SHU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.3   pp.594-597
Publication Date: 2019/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.594
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
covering radius,  Reed-Muller codes,  third-order nonlinearity,  Boolean function,  

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Summary: 
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 [1] 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.