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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/2603.08213 |
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| _version_ | 1866912955074871296 |
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| author | Rabefihavanana, Luc Andriatahiny, Harinaivo Ferdinand, Randriamiarampanahy |
| author_facet | Rabefihavanana, Luc Andriatahiny, Harinaivo Ferdinand, Randriamiarampanahy |
| contents | In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in minimum distance, decoding efficiency, and structural simplicity. By combining the hypergraph product framework with a generalized Shor construction, we obtain a scalable class of quantum codes with parameters $[[6k^2,\, k^2,\, d]]$. The resulting quantum codes exhibit a rich combinatorial structure and promising properties, particularly in terms of locality, low-density parity-check (LDPC) structure, and asymptotic behavior. The minimum distance satisfies $d=3$ for $k=3$ and $d=4$ for $k\ge4$, establishing a new framework for structured quantum LDPC code design and optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08213 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of a Family of Quantum Codes Using Sub-exceding Functions via the Hypergraph Product and the Generalized Shor Construction Rabefihavanana, Luc Andriatahiny, Harinaivo Ferdinand, Randriamiarampanahy Quantum Physics In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in minimum distance, decoding efficiency, and structural simplicity. By combining the hypergraph product framework with a generalized Shor construction, we obtain a scalable class of quantum codes with parameters $[[6k^2,\, k^2,\, d]]$. The resulting quantum codes exhibit a rich combinatorial structure and promising properties, particularly in terms of locality, low-density parity-check (LDPC) structure, and asymptotic behavior. The minimum distance satisfies $d=3$ for $k=3$ and $d=4$ for $k\ge4$, establishing a new framework for structured quantum LDPC code design and optimization. |
| title | Construction of a Family of Quantum Codes Using Sub-exceding Functions via the Hypergraph Product and the Generalized Shor Construction |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.08213 |