Robust codes creation based on bent-functions and wavelet transformation

Abstract

Subject of Research. This paper presents an application of wavelet transformation and bent-functions in the creation of non-linear robust codes. The usage of wavelet decompositions gives the possibility to create a large number of different designs of robust codes. Method. To improve the non-linear properties of robust codes, bent-functions were used in the construction. Thereby the maximum non-linearity of functions is ensured increasing the probability of detecting an error in the data channel. Different designs of codes based on wavelet transform and bent-functions are developed. The difference of constructions consists in the usage of different grids for wavelet transformation: a grid with static values, or a grid based on an incoming information word. The existing linear and non-linear codes were analyzed, their comparison with the developed codes was performed.Main Results. The developed designs are robust codes and have higher characteristics compared to existing designs of robust codes. The maximum probability of the error masking for the developed designs is 0.46875. This result is a better one compared to the existing reliable Kerdock code and enables better protection against side-channel attacks. Practical Relevance. These code designs can be used in the tasks to ensure the security of information transmitted.