On linear complexity of periodic sequences over extension fields from cyclic difference sets

The set of constant-weight sequences over GF(q) from the cyclic difference set generalized by the authors are considered. For the linear complexity(LC) of infinite sequences with their one period as an element in the set, we give a conjecture that LCs of all sequences except two in the set are the maximum as same as their period and LCs of remaining two sequences are the maximum value minus one. Five numerical examples over two prime fields and three non-prime(extension) fields are shown for evidences of main conjecture in this paper.