A Direct Construction of Complete Complementary Codes With Arbitrary Lengths
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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.
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