In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this letter, a class of four-weight binary cyclic codes are presented. Their weight distributions of these cyclic codes are also settled.