The Fourier spectrum

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Across
  1. 5. What is a Boolean function where the number of 1 equals the number of zeros? (...(Boolean function))
  2. 9. What degree of the Hadamard matrix is used in the Fourier transform?
  3. 12. What kind of Boolean functions can S-boxes be represented with?
  4. 13. What is the parity of all other coefficients if one of coefficient equals 3?
  5. 16. What process of Boolean function analysis can the Fourier spectrum be involved in?
  6. 17. How can a Boolean function be defined with the Fourier spectrum?
  7. 18. what does the Fourier transform of a Boolean function generate?
  8. 19. What metric is used in the linearization process?
Down
  1. 1. Which of the Fourier coefficients is the sum of ones in the table representation of a Boolean function?
  2. 2. how is the transform called which is one of the natural decomposition of a Boolean function?
  3. 3. What is the name of the scientist after whom the transform’s matrix is named?
  4. 4. What is the name of one of two scientists after whom the more convenient transform for analysis than the Fourier one is named?
  5. 6. What is the part of the information security where the Fourier transform is used in?
  6. 7. How in other words can we name getting the Fourier spectrum?
  7. 8. what is the most probable value of the Fourier coefficient?
  8. 10. what is a function, mapping from n-dimensional vector space to {0, 1}?
  9. 11. How is the number in the Fourier spectrum called?
  10. 14. which vectors does a Boolean function convert?
  11. 15. Whatis the parity of all other coefficients if one of coefficient equals 4?
  12. 18. How can we call the first Fourier coefficient?