N-Shift Cross-Orthogonal Sequences and Complete Complementary Codes

N-shift cross-orthogonal sequences are powerful materials for constructing complete complementary codes. In this paper, we present six theorems concerning general construction and expansion methods with the least upper bounds for N-shift cross-orthogonal sequences and complete complementary codes. Applying the theorems that about construction and expansion method of N-shift cross-orthogonal sequences, many types of N-shift cross orthogonal sequences are constructed systematically. Those include the sequence sets consisting of different lengths and include previous classes as special cases. Based on the generated N-shift cross orthogonal sequences, a complete complementary code are constructed by the theorem of construction method of complete complementary code. The last theorem which is about expansion method of complete complementary code are given for increase the number of sequence sets.