Preprint Mathematics
Independent Squares and Average-Radius Obstructions for Linear Codes
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Overview
Abstract
Independent affine squares yield binary-input average-radius list-recovery obstructions for linear codes over finite fields. The paper proves an exact two-fiber certificate cost, develops unequal shortening groups, and gives sixteen-word folded Reed–Solomon constructions with mean relative error 3/4. Complete proofs, three certificates, and a portable reproduction package accompany the manuscript.
Keywords average-radius list recovery · linear codes · folded Reed–Solomon codes · independent affine squares · two-fiber certificates
Scope of the work
Linear codes over finite fields, binary input lists, independent-square profiles, and standard full-length folded Reed–Solomon realizations.
Reproduction notes
The downloadable package includes the manuscript, LaTeX source, three certificates, standard-library reproduction scripts, and saved verification receipts.
The manuscript
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The complete manuscript, as published in this edition.
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Cite this edition
Scott Schubr. (2026). Independent Squares and Average-Radius Obstructions for Linear Codes (Version 1). Luminary Research Archive. https://luminaryoddities.com/researcharchive/independent-squares-average-radius-obstructions-linear-codes/v/1
BibTeX
@techreport{luminary_independent_squares_average_radius_obstructions_linear_codes_v1,
title = {Independent Squares and Average-Radius Obstructions for Linear Codes},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Preprint},
note = {Version 1},
url = {https://luminaryoddities.com/researcharchive/independent-squares-average-radius-obstructions-linear-codes/v/1}
}Reader correspondence
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