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Research Article · Preprint Mathematics

Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codes

Scott Schubr

  • Mathematics
  • Coding Theory
Primary subject
Mathematics
Subject subfields
Coding Theory
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
1 · Permanent link
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Overview

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.

Keywords folded Reed–Solomon codes · list recovery · affine configurations · fiber certificates · folded Wronskian

Scope of the work

The main certificate applies to eight points over arbitrary fields. The general sixteen-point bound and output-cap-fifteen extension remain open. The coding result is a list-size bound; it does not supply a new decoding algorithm.

Reproduction notes

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.

The manuscript

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Cite this edition

Scott Schubr. (2026). Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codes (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/eight-point-fiber-certificates-binary-input-list-recovery-folded-reed-solomon-codes/v/1

BibTeX
@techreport{luminary_eight_point_fiber_certificates_binary_input_list_recovery_folded_reed_solomon_codes_v1,
  title = {Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codes},
  author = {Scott Schubr},
  year = {2026},
  institution = {Luminary Research Archive},
  type = {Research Article},
  note = {Version 1},
  url = {https://research.luminaryoddities.com/eight-point-fiber-certificates-binary-input-list-recovery-folded-reed-solomon-codes/v/1}
}

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