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Combinatorial t-designs from special functions

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Abstract

A special function is a function either of special form or with a special property. Special functions have interesting applications in coding theory and combinatorial t-designs. The main objective of this paper is to survey t-designs constructed from special functions, including quadratic functions, almost perfect nonlinear functions, almost bent functions, bent functions, bent vectorial functions, and planar functions. These combinatorial designs are not constructed directly from such functions, but come from linear codes which are constructed with such functions. As a byproduct, this paper also surveys linear codes from certain special functions.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Cunsheng Ding

  2. The School of Mathematics and Information, China West Normal University, Nanchong, 637002, China

    Chunming Tang

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  1. Cunsheng Ding
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  2. Chunming Tang
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Correspondence to Chunming Tang.

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This article belongs to the Topical Collection: Boolean Functions and Their Applications IV

Guest Editors: Lilya Budaghyan and Tor Helleseth

C. Ding’s research was supported by the Hong Kong Research Grants Council, Proj. No. 16300418. C. Tang was supported by National Natural Science Foundation of China (Grant No. 11871058) and China West Normal University (14E013, CXTD2014-4 and the Meritocracy Research Funds).

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Ding, C., Tang, C. Combinatorial t-designs from special functions. Cryptogr. Commun. 12, 1011–1033 (2020). https://doi.org/10.1007/s12095-020-00442-2

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  • DOI: https://doi.org/10.1007/s12095-020-00442-2

Keywords

Mathematics Subject Classification 2010