Galois equiangular tight frames from Galois self-dual codes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913950755454976 |
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| author | An, Junmin Kim, Jon-Lark |
| author_facet | An, Junmin Kim, Jon-Lark |
| contents | Greaves et al. (2022) extended frames over real or complex numbers to frames over finite fields. In this paper, we study the theory of frames over finite fields by incorporating the Galois inner products introduced by Fan and Zhang (2017), which generalize the Euclidean and Hermitian inner products. We define a class of frames, called Galois frames over finite fields, along with related notions such as Galois Gram matrices, Galois frame operators, and Galois equiangular tight frames (Galois ETFs). We also characterize when Galois self-dual codes induce Galois ETFs. Furthermore, we construct explicitly Galois ETFs from Galois self-dual constacyclic codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Galois equiangular tight frames from Galois self-dual codes An, Junmin Kim, Jon-Lark Information Theory 51E22, 94B05 Greaves et al. (2022) extended frames over real or complex numbers to frames over finite fields. In this paper, we study the theory of frames over finite fields by incorporating the Galois inner products introduced by Fan and Zhang (2017), which generalize the Euclidean and Hermitian inner products. We define a class of frames, called Galois frames over finite fields, along with related notions such as Galois Gram matrices, Galois frame operators, and Galois equiangular tight frames (Galois ETFs). We also characterize when Galois self-dual codes induce Galois ETFs. Furthermore, we construct explicitly Galois ETFs from Galois self-dual constacyclic codes. |
| title | Galois equiangular tight frames from Galois self-dual codes |
| topic | Information Theory 51E22, 94B05 |
| url | https://arxiv.org/abs/2507.15448 |