On cyclotomic generator of order r
Information Processing Letters
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Autocorrelation of Legendre-Sidelnikov sequences
IEEE Transactions on Information Theory
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We generalize the Legendre-Sidelnikov sequence to d-ary balanced sequence by using multiplicative character, where d is a common divisor of p−1 and q−1; p is an odd prime and q a power of an odd prime, and $\gcd(p,q-1)=1$. Then with character sums we analyze some important pseudorandomness measures including (aperiodic) autocorrelation, power correlation of measure of order k, and linear complexity profile. Results show that aperiodic autocorrelation and power correlation measure of order 2 are ideal in terms of order of magnitude of a good pseudorandom sequence.