On a conjectured ideal autocorrelation sequence, a related triple-error correcting 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 autocorrelation property. In the present correspondence it is shown that each such sequence is balanced and, moreover, that the dual of the linear cyclic code generated by the sequence and its cyclic shifts, is a triple-error correcting code having the same weight distribution as the triple-error correcting 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.