The generalized cyclotomic sequence of order two has several good randomness properties and behaves like the Legendre sequence in several aspects. We calculate the autocorrelation values of the generalized cyclotomic sequence of order two. Our result shows that this sequence could have very good autocorrelation property and pattern distributions of length two if the two primes are chosen properly.

/pdf/autocorrelation-values-of-generalized-cyclotomic-sequences-1arl4csflz.pdf

Autocorrelation values of generalized cyclotomic sequences of order two

https://www.cse.ust.hk/faculty/cding/JOURNALS/ffa111.pdf

Permutation polynomials over finite fields from a powerful lemma

In this correspondence, the linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are determined. Our results show that these sequences also have high linear complexity.

Linear complexity of new generalized cyclotomic sequences of order two of length pq

https://www.cse.ust.hk/faculty/cding/Sequence/binseq2.pdf

Binary sequences with optimal autocorrelation

A high linear complexity profile is a desirable feature of sequences used for cryptographical purposes. For a given binary sequence we estimate its linear complexity profile in terms of the correlation measure, which was introduced by Mauduit and Sarkozy. We apply this result to certain periodic sequences including Legendre sequences, Sidelnikov sequences and other sequences related to the discrete logarithm.

Linear complexity profile of binary sequences with small correlation measure

We determine the linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence. The result shows that Legendre sequences are quite good from the linear complexity viewpoint.

T. Hesseseth

Papers

On the linear complexity of Legendre sequences