Perfect Gaussian Integer Sequences of Odd Period <formula formulatype="inline"><tex Notation="TeX">${2^m} - 1$</tex> </formula>

Abstract

In this letter, some perfect Gaussian integer sequences of period ${2^m} - 1$ are proposed based on the trace representations of Legendre sequences, Hall’s sextic residue sequences, $m$ -sequences, and Gordon-Mills-Welch (GMW) sequences over the finite field ${{\BBF}_{{2^m}}}$ . Moreover, the energy efficiency of these sequences is approximately 1 for sufficiently large $m$ .