Elliptic Curve Quaternary Sequences Constructed Using the Reverse Gray Mapping

Quaternary sequences are the most important sequences in view of many practical applications. Using the reverse Gray mapping, we propose a new construction of elliptic curve quaternary sequences with strong pseudorandom properties. We apply a result of Marzouk and Winterhof on the relation between the pseudorandom measures for binary sequences and the measures for quaternary sequences to analyze the well-distribution measure and correlation measure of order l, which were introduced by Mauduit and Sárközy, for the proposed sequences.