A Direct Construction of Complete Complementary Codes With Arbitrary Lengths
share
This paper is focused on efficient design of complete complementary codes (CCCs) which have found wide applications in coding, signal processing and wireless communication due to their zero auto- and cross-correlation sum properties. A major motivation of this research is that the existing state-of-the-art can generate CCCs with certain lengths only and therefore may not meet the diverse requirements in practice. We introduce a new tool called multivariable functions and propose a direct construction of CCCs with any arbitrary lengths in the form ∏_i=1^k p_i^m_i, where k is a positive integer, p_1,p_2,,p_k are prime numbers and m_1,m_2,,m_k are positive integers whose sum is not less than 1. For k=1 and p_1=2, our proposed generator reduces to the exact Golay-Davis-Jedwab (GDJ) sequence generator as a special case. For k>1 and p_1=p_2=⋯=p_k=2, it gives rise to the conventional CCCs with power-of-two lengths which are obtained from generalized Boolean functions.
READ FULL TEXT
