Totally symmetric Grassmannian codes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915747644571648 |
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| author | Fickus, Matthew Iverson, Joseph W. Jasper, John Mixon, Dustin G. |
| author_facet | Fickus, Matthew Iverson, Joseph W. Jasper, John Mixon, Dustin G. |
| contents | We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs), which consequently form optimal Grassmannian codes. By virtue of their construction, our EITFFs have the remarkable property of total symmetry: any permutation of subspaces can be achieved by an appropriate unitary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19542 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Totally symmetric Grassmannian codes Fickus, Matthew Iverson, Joseph W. Jasper, John Mixon, Dustin G. Combinatorics Information Theory Functional Analysis Group Theory We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs), which consequently form optimal Grassmannian codes. By virtue of their construction, our EITFFs have the remarkable property of total symmetry: any permutation of subspaces can be achieved by an appropriate unitary. |
| title | Totally symmetric Grassmannian codes |
| topic | Combinatorics Information Theory Functional Analysis Group Theory |
| url | https://arxiv.org/abs/2406.19542 |