Abstract
We give a short direct proof for a famous theorem published by Kasami in 1971. In terms of Walsh analysis it states that for d = 22k - 2k + 1 the Walsh spectrum of the Boolean function Tr(x d) on GF(2n) consists precisely of the three values 0, ±2(n+s)/2 if s = gcd(k, n) = gcd(2k, n).
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Dobbertin, H. Another Proof of Kasami's Theorem. Designs, Codes and Cryptography 17, 177–180 (1999). https://doi.org/10.1023/A:1026475109375
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DOI: https://doi.org/10.1023/A:1026475109375