Some results on apn functions and weakly regular bent functions over finite fields

Date

2023-7

Author

Acunalp Erleblebici, İlksen

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In this thesis, we present our work on Carlet’s bivariate APN construction and representations of APN power functions. We report necessary and sufficient conditions on some families of bivariate APN functions and our observations about the representation of the APN power functions by following the methods given by Calderini et al. in 2021 and Budaghyan et al. in 2022 and we give some computational results on this research. On the other hand, we study the application of cryptographic functions in coding theory, and we derive several linear codes with good parameters by employing weakly regular bent functions over the finite fields of odd characteristics.

Subject Keywords

APN functions, bivariate APN construction, APN power functions, linear code, weight distribution, weakly regular bent function

URI

https://hdl.handle.net/11511/105348

Collections

Graduate School of Applied Mathematics, Thesis