Notes about imbalance and arithmetic autocorrelation of N -ary half- l -sequences
Vladimir Edemskiy · Cryptologia · 2025
In this paper, we study the imbalance of N-ary half-l-sequences as well as their arithmetic autocorrelation. The arithmetic correlation or “with-carry” correlation is an analog of the classical correlation of sequences. We obtain three families of N-ary half-l-sequences with ideal arithmetic autocorrelation in the case when the connection number of sequences is not a power of a prime. Also, it is shown that in many other cases there are no balanced N-ary half-l-sequences with ideal arithmetic autocorrelation. Our method is based on the properties of sums of Legendre symbols.