Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codes
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Abstract
For eight distinct points over an arbitrary field, we construct a finite nonnegative rational certificate bounding the total population of the two largest fibers of every linear quotient. The certificate has intercept two and dimension cost at most nine, attained by the Boolean three-cube. A folded-Wronskian argument gives an average-radius list-recovery bound for primitive-power folded Reed–Solomon codes with input lists of size two and output cap seven. Supporting results treat structured sixteen-point configurations.
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- main.pdf114.5 KiB · pdf
SHA-256
91bf528ee8cd09b729526f4b22baa6c3f85dd9a98e4fcc6d9faa4dc035efe1b3 - main.tex1.0 KiB · source
SHA-256
9276f152de42c28422c860e99194aed34e8a34c0866ad4336ae69f3a6e7444d9 - Eight-point-fiber-certificates-edition-1-privacy-corrected-20261019.zip128.4 KiB · package
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7340d4465e0e0078e9e3d0d909584333772ff43f143574f3ff629796c6deb316 - SHA256_RECEIPT.json1.5 KiB · manifest
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866d53abaf1eabbcc9cc74eb5979dd68f0a00389ecf7ac0e038ee902f6ac2376
Available editions
Research details
- Subjects
- Mathematics · Coding Theory
- Keywords
- folded Reed–Solomon codes, list recovery, affine configurations, fiber certificates, folded Wronskian
- Manuscript date
- 2026-10-18
- Reader reuse
- No additional permission granted
Scope
The main certificate applies to eight points over arbitrary fields. The coding result is a list-size bound.
Reproduction
The complete package contains the eleven-page manuscript, LaTeX source, analytic proof and checksum receipt. Historical finite diagnostic evidence is documented in the package; the general statements rest on the analytic proof.
Publication package corrected to contain publication materials only. The manuscript and edition are unchanged.