New Constructions of Binary Two-Dimensional CCC of Length Non-Power of Two

This letter introduces an efficient method for constructing two-dimensional (2D) complete complementary codes (CCCs) with novel non-power-of-two lengths, addressing a major limitation of existing direct constructions. Specifically, we construct 2D-CCCs of array sizes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^{n} \times 10 \cdot 2^{m-4}$</tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m \geq 4, n \in \mathbb {Z}^+$</tex-math></inline-formula>) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^{n} \times 26 \cdot 2^{m-5}$</tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m \geq 5, n \in \mathbb {Z}^+$</tex-math></inline-formula>) using generalized Boolean functions (GBFs). Binary 2D-CCCs are especially beneficial in spread spectrum communication due to their simple modulo-2 arithmetic, modulation, and correlation characteristics. Additionally, our construction unifies and generalizes existing results, as 2D-CCCs with power-of-two lengths and one-dimensional (1D) CCCs naturally emerge as special cases. Thus, our work not only advances the field but also contributes to the literature related to the direct construction of binary 2D-CCCs.