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Exact Storage-Repair-Bandwidth Tradeoffs for (6,5,5) and (7,6,6) Exact-Repair Regenerating Codes

  • Chao Tian
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Abstract

This note provides exact information-theoretic outer bounds that completely characterize the storage-repair-bandwidth tradeoff regions for the cases (n,k,d)=(6,5,5) and (7,6,6). The layered code proposed by Tian et al. achieves the tradeoff and is thus optimal. GPT-6 Astra assisted in the discovery of these bounds, based on a new conditioning argument and a structured search over the restricted subsets of entropy linear program constraints. The proofs are given as exact integer-valued certificates, which are difficult for direct human verification, and a Python verifier is included as part of the package, together with the certificates.

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Cite

BibTeXRIS
BibTeX
@misc{tian2026exact,
  title = {{Exact Storage-Repair-Bandwidth Tradeoffs for $(6,5,5)$ and $(7,6,6)$ Exact-Repair Regenerating Codes}},
  author = {Chao Tian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28199},
  eprint = {2610.28199},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28199},
}
RIS
TY  - UNPB
TI  - Exact Storage-Repair-Bandwidth Tradeoffs for (6,5,5) and (7,6,6) Exact-Repair Regenerating Codes
AU  - Chao Tian
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28199
UR  - https://arxiv.org/abs/2610.28199
AB  - This note provides exact information-theoretic outer bounds that completely characterize the storage-repair-bandwidth tradeoff regions for the cases (n,k,d)=(6,5,5) and (7,6,6). The layered code proposed by Tian et al. achieves the tradeoff and is thus optimal. GPT-6 Astra assisted in the discovery of these bounds, based on a new conditioning argument and a structured search over the restricted subsets of entropy linear program constraints. The proofs are given as exact integer-valued certificates, which are difficult for direct human verification, and a Python verifier is included as part of the package, together with the certificates.
ER  -