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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.22606 |
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| _version_ | 1866915610320961536 |
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| author | Garg, Sumegha Sudan, Madhu Wu, Gabriel |
| author_facet | Garg, Sumegha Sudan, Madhu Wu, Gabriel |
| contents | Motivated by recent advances in locally testable codes and quantum LDPCs based on robust testability of tensor product codes, we explore the local testability of tensor products of (an abstraction of) algebraic geometry codes. Such codes are parameterized by, in addition to standard parameters such as block length $n$ and dimension $k$, their genus $g$. We show that the tensor product of two algebraic geometry codes is robustly locally testable provided $n = Ω((k+g)^2)$. Apart from Reed-Solomon codes, this seems to be the first explicit family of two-wise tensor codes of high dual distance that is robustly locally testable by the natural test that measures the expected distance of a random row/column from the underlying code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing Tensor Products of Algebraic Codes Garg, Sumegha Sudan, Madhu Wu, Gabriel Information Theory Motivated by recent advances in locally testable codes and quantum LDPCs based on robust testability of tensor product codes, we explore the local testability of tensor products of (an abstraction of) algebraic geometry codes. Such codes are parameterized by, in addition to standard parameters such as block length $n$ and dimension $k$, their genus $g$. We show that the tensor product of two algebraic geometry codes is robustly locally testable provided $n = Ω((k+g)^2)$. Apart from Reed-Solomon codes, this seems to be the first explicit family of two-wise tensor codes of high dual distance that is robustly locally testable by the natural test that measures the expected distance of a random row/column from the underlying code. |
| title | Testing Tensor Products of Algebraic Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2410.22606 |