Constructions of $q$-ary Golay Complementary Pairs Over Flexible Non-Power-of-Two Lengths
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| Format: | Preprint |
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2026
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| _version_ | 1866917412991926272 |
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| author | Yang, Zhiye Feng, Keqin |
| author_facet | Yang, Zhiye Feng, Keqin |
| contents | 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 $\textit{A}_i,\textit{B}_i\in\{ξ^a:0\leq a\leq q-1\}$ with $ξ=e^{\frac{2π\sqrt{-1}}{q}}$.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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14667 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructions of $q$-ary Golay Complementary Pairs Over Flexible Non-Power-of-Two Lengths Yang, Zhiye Feng, Keqin Information Theory 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 $\textit{A}_i,\textit{B}_i\in\{ξ^a:0\leq a\leq q-1\}$ with $ξ=e^{\frac{2π\sqrt{-1}}{q}}$.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. |
| title | Constructions of $q$-ary Golay Complementary Pairs Over Flexible Non-Power-of-Two Lengths |
| topic | Information Theory |
| url | https://arxiv.org/abs/2604.14667 |