On the linear complexity of Hall’s sextic residue sequences over $${ GF}(q)$$ G F ( q )

Abstract

In this paper, we derive the linear complexity of Hall’s sextic residue sequences over the finite field of odd prime order. The order of the field is not equal to a period of the sequence. Our results show that Hall’s sextic residue sequences have high linear complexity over the finite field of odd order. Also we estimate the linear complexity of series of generalized sextic cyclotomic sequences. The linear complexity of these sequences is larger than half of the period.