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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14895 |
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| _version_ | 1866909043879051264 |
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| author | Dhankhar, Priya Singh, Sanjay Kumar |
| author_facet | Dhankhar, Priya Singh, Sanjay Kumar |
| contents | In this paper, we investigate generalized bent functions (GBFs) from $\mathbb{Z}_3^n$ to $\mathbb{Z}_m$. We show that GBFs exist whenever $3$ divides $m$, while several nonexistence results are obtained when $3\nmid m$. In particular, we prove that no GBFs exist for $n=1,2$ when $m$ is odd and not divisible by $3$. For the case $n=3$, we establish the nonexistence of GBFs $f:\mathbb{Z}_3^3 \rightarrow \mathbb{Z}_{5\cdot11^r}$ for all nonnegative integers $r$. Finally, we show that no GBF exists from $\mathbb{Z}_3$ to $\mathbb{Z}_{2m'}$ and $\mathbb{Z}_3^2$ to $\mathbb{Z}_{2m'}$, where $m'$ is odd and not divisible by $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonexistence results of generalized bent functions from $\mathbb{Z}_3^n$ to $ \mathbb{Z}_m$ Dhankhar, Priya Singh, Sanjay Kumar Combinatorics 11A07, 16S34, 05B10, 94A15 In this paper, we investigate generalized bent functions (GBFs) from $\mathbb{Z}_3^n$ to $\mathbb{Z}_m$. We show that GBFs exist whenever $3$ divides $m$, while several nonexistence results are obtained when $3\nmid m$. In particular, we prove that no GBFs exist for $n=1,2$ when $m$ is odd and not divisible by $3$. For the case $n=3$, we establish the nonexistence of GBFs $f:\mathbb{Z}_3^3 \rightarrow \mathbb{Z}_{5\cdot11^r}$ for all nonnegative integers $r$. Finally, we show that no GBF exists from $\mathbb{Z}_3$ to $\mathbb{Z}_{2m'}$ and $\mathbb{Z}_3^2$ to $\mathbb{Z}_{2m'}$, where $m'$ is odd and not divisible by $3$. |
| title | Nonexistence results of generalized bent functions from $\mathbb{Z}_3^n$ to $ \mathbb{Z}_m$ |
| topic | Combinatorics 11A07, 16S34, 05B10, 94A15 |
| url | https://arxiv.org/abs/2605.14895 |