In this letter we first introduce a new generalized cyclotomic sequence of order four with respect to pq, then we calculate the linear complexity and minimal polynomial of this sequence. Our results show that the new binary sequence is quite good from the linear complexity viewpoint.

In this letter, we introduce the concept of k-error lattice structure to describe the stability of lattice structure for pseudorandom number sequences, give some of its properties, and make a study of the relationship between the k-error lattice structure and the k-error linear complexity. These properties and the relationship create an elementary framework to study the stability of the lattice structure of pseudorandom number sequences.

In their paper, G. Gong and S.Q. Jiang construct a new pseudo-random sequence generator by using two ternary linear feedback shift registers (LFSR). The new generator is called an editing generator which a combined model of the clock-controlled generator and the shrinking generator. For a special case (Both the base sequence and the control sequence are mm-sequence of degree n), the period, linear complexity, symbol distribution and security analysis are discussed in the same article. In this paper, we expand the randomness results of the edited sequence for general cases, we do not restrict the base sequence and the control sequence has the same length. For four special cases of this generator, the randomness of the edited sequence is discussed in detail. It is shown that for all four cases the editing generator has good properties, such as large periods, high linear complexities, large ratio of linear complexity per symbol, and small un-bias of occurrences of symbol. All these properties make it necessary to resist to the attack from the application of Berlekamp-Massey algorithm.