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Vectorial Resilient $PC(l)$ of Order $k$ Boolean Functions from AG-Codes

Hao Chen·Liang Ma·Jianhua Li
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Abstract

Propagation criterion of degree $l$ and order $k$ ($PC(l)$ of order $k$) and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1, 2, 3,6, 7,8,10,11,16]. Kurosawa, Stoh [8] and Carlet [1] gave a construction of Boolean functions satisfying $PC(l)$ of order $k$ from binary linear or nonlinear codes in. In this paper, algebraic-geometric codes over $GF(2^m)$ are used to modify Carlet and Kurosawa-Satoh's construction for giving vectorial resilient Boolean functions satisfying $PC(l)$ of order $k$. The new construction is compared with previously known results.

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Hao Chen, Liang Ma, Jianhua Li. 2006-09-19. Vectorial Resilient $PC(l)$ of Order $k$ Boolean Functions from AG-Codes. https://arxiv.org/abs/cs/0606011

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