Global Navigation Satellite Systems (GNSSs) typically use low-correlation sequences that have length related to the common clock frequency of 10.23 MHz. In particular, operations in the $L1$ frequency band, of two major GNSS systems, the Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS), employ spreading sequences having length 10230. In these two systems, the length 10230 is achieved by padding and truncating respectively, a family of Weil sequences having period that is a prime number, either 10223 or 10243. As is well known, either truncation or padding leads in general, to a degradation in correlation performance. In the present paper, we adopt a different approach, and present the design of a family of Interleaved $Z_{4}$-linear (IZ4) sequences having period exactly equal to 10230. Closed-form expressions for the correlation properties of the sequence family are included. The balance and even-correlation performance of the new family equals or improves upon the corresponding performance of the GPS and BDS signal sets. In particular, the new IZ4 family has maximum even cross-correlation value that is better by 4.4 dB, than that of the truncated or padded Weil sequences employed in these two systems. The sequence family also turns in comparable odd-correlation performance. The sequences can be generated using a simple, shift-register-based implementation presented here.