On a conjectured ideal autocorrelation sequence and a related triple-errorcorrecting cyclic code

In a recent paper, No, Golomb, Gong, Lee, and Gaal conjectured that certain binary sequences having a simple trace description possess the ideal autoc orrelation property. In the present correspondence it is shown that each su ch sequence is balanced and, moreover, that the dual of the linear cyclic c ode generated by the sequence and its cyclic shifts, is a triple-error corr ecting code having the same weight distribution as the triple-error correct ing Bose-Chaudhuri-Hocquenghem (BCH) code. This cyclic code also contains a cyclic subcode that yields a new family of sequences having the same size and correlation parameters as does the family of Gold sequences.