On the Weight and Nonlinearity of Boolean Functions: A Matrix-Based Approach.
Joseph Nelson, Chungath Srinivasan, Sree Parvathi P M
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Source: Crossref
Published: Jan 1, 2026
DOI: 10.69793/ijmcs/04.2026/nsp
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In this paper, we present a matrix-based approach for studying Boolean functions using tools from linear algebra and set theory. We investigate the relationship between matrix rank, Hamming weight, and nonlinearity, and use this framework to characterize and count classes of Boolean functions whose weight equals their nonlinearity. In particular, we determine the number of Boolean functions satisfying wt(f)=nl(f)=2^{n-2}+1 and develop a rank-based method for constructing Boolean functions with prescribed nonlinearity. The results provide an alternative perspective for analyzing Boolean functions and lead to an open problem connecting maximum nonlinearity with a rank-related problem in linear algebra.
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