Ideal Sequence Couple Design for Split Circle Classes with Different Cycle Lengths

The split-circle class and the generalized split-circle class are commonly utilized mathematical tools in sequence design. They have been extensively applied in the study of construction methods for almost different set couples and ideal sequence couples. In this paper, on the basis of sequence couplings and difference set couplings, the finite field, and Chinese remainder theorem are utilized to combine computers to carry out the design of the generalized subcircle class construction algorithm, and based on this algorithm, the search algorithm for sequence couplings is designed. In addition, based on the theory of fractional circle classes and fractional circle numbers, the article integrates the equivalence relations between difference families and ideal balanced binary almost complementary pairs. Then, it obtains the ideal sequence even construction method based on fractional circle classes. For the effectiveness of the sequence couple search algorithm, a search experiment is set up with a binary sequence couple as an example. Its efficiency is analyzed in comparison with that based on the difference table and the bit operation, and an example of the ideal sequence couple construction under different cycle lengths is analyzed based on the construction method. The search algorithm combined with the generalized fractional circle class can obtain the data sequences of optimal binary sequence couple pairs, pseudo-random binary sequence couples, and ideal three-valued autocorrelated binary sequence couples. The average computational efficiency of the algorithm is within 13ms and 3 when both s ≡ 1 (mod 4) and s ≡ 3 (mod 4), and the parameters of the binary and quadratic periodic ideal sequence couples obtained by the algorithm meet the parameters of (10,2,5)LACSP₃⁴ when Z takes the value of 2 or R_x1 (γ) = –1 + 2t, respectively. Carrying out the construction of perfect sequence couples under different cycle lengths with the generalized fractional circle class the construction of ideal sequence couplings with varying lengths of cycle in the generalized fractional circle class can obtain a variety of forms of sequence coupling data, which enhances the application range of ideal sequence couplings.