On the complexity of a family of Legendre sequences with irreducible polynomials

Ahlswede, Khachatrian, Mauduit and Sárközy [1] introduced the f-complexity measure (“f” for family) in order to study pseudorandom properties of large families of binary sequences. So far several families have been studied by this measure. In the present paper I considerably improve on my earlier result in [8], where the f  -complexity measure of a family based on the Legendre symbol and polynomials over FpFp is studied. This paper also extends the earlier results to a family restricted on irreducible polynomials.