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arXiv · 2604.14667

Constructions of $q$-ary Golay Complementary Pairs Over Flexible Non-Power-of-Two Lengths

Zhiye Yang·Keqin Feng
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Abstract

Golay complementary pair (GCP), first introduced by Golay in 1951, has been extensively studied and widely applied in communication systems. A $q$-ary GCP $\{\mathbf{A},\mathbf{B}\}$ consists of two $q$-ary complex sequences $\mathbf{A}=(A_0,\cdots,A_{M-1})$ and $\mathbf{B}=({B}_0,\cdots,{B}_{M-1})$ of equal length $M$, where $\textit{A}_i,\textit{B}_i\in\{\xi^a:0\leq a\leq q-1\}$ with $\xi=e^{\frac{2\pi\sqrt{-1}}{q}}$.In this paper,we prove that the existence of a quaternary ($q=4$) GCP of length $M$ is equivalent to the explicit constructibility of ($4h$)-ary GCPs of length $2^mM$ for all integers $h,m\geq1$. All proposed sequences are constructed via extended Boolean functions (EBFs), and the direct construction yields GCPs with more flexible length ranges than all previous relevant results.

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Zhiye Yang, Keqin Feng. 2026-04-16. Constructions of $q$-ary Golay Complementary Pairs Over Flexible Non-Power-of-Two Lengths. https://arxiv.org/abs/2604.14667

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