On pseudorandom sequences of $$k$$ k symbols constructed using finite fields

Abstract

A family of pseudorandom sequences of $$k$$ k symbols are constructed by using finite fields of prime-power order. The construction is an extension of certain construction of Sarkozy and Winterhof on binary sequences using the quadratic character with polynomial arguments over any finite fields, and of certain construction of Ahlswede, Mauduit and Sarkozy on sequences of $$k$$ k symbols using multiplicative characters with polynomial arguments over finite prime fields. Certain pseudorandom measures of the resulting sequences are considered.