Ahlswede, Khachatrian, Mauduit and Sárközyy 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 [7], where the f-complexity measure of a family based on the Legendre symbol and polynomials over Fp is studied. This paper also extends the earlier results to a family restricted on irreducible polynomials
