A class of new binary pseudo random noise (PRN) sequences based on the Sidenikov, Lempel, Choen, Eastman (SLCE) sequences is proposed for Global Navigation Satellite System (GNSS) use. The Weil-like WSLCE sequences have more extra advantages with good correlation properties over SLCE sequences, such as larger quantities of spreading codes to be selected. An effective optimization strategy on WSLCE sequences is introduced and the spreading codes for BeiDou B1C signal potential use is acquired according to this strategy. Even autocorrelation and cross-correlation values of the WSLCE spreading codes are almost 5 dB better than that of Galileo E1-OS signal, and their intersystem cross-correlation denoting two different GNSSs compatibility only deteriorates within 0.2 dB in a probability of 99.99%.