New Constructions of Complementary Sets of Sequences of Lengths Non-Power-of-Two

Abstract

The construction of complementary sets (CSs) of sequences with different set sizes and sequence lengths become important due to the practical application in orthogonal frequency-division multiplexing (OFDM) systems. Most of the constructions of CSs based on generalized Boolean functions (GBFs) are of length 2α (α is the non-negative integer). Recently, some works have reported on the construction of CSs having lengths non-power of two, i.e., in the form of 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-1</sup> + 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sup> (m is the non-negative integer, 0 ≤ v <; m). In this letter, we propose the constructions of CSs of lengths N +1 and N +2 for set size 4n, and CSs of length 2N + 3 for set size 8n, by employing the insertion method on Golay complementary pairs of length N. This systematic construction can generate more CSs of the new sequence length and set size, which has not been reported before.