Independent Squares and Average-Radius Obstructions for Linear Codes
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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.
Read the full paper in the original PDF.
Edition files
- independent_squares_average_radius.pdf149.2 KiB · pdf
SHA-256
1bf2db9cc656db93bdca29f7dee6e2804d19755e189590bbb5f9e5a6f638650c - main.tex43.6 KiB · source
SHA-256
1ae168bdbaa3f1655ce824d561410812a5001481c07d2bed1b79e67535a0508e - Independent-squares-edition-1-privacy-corrected-20261019.zip211.7 KiB · package
SHA-256
a594a4934e35dbd86f4d9ae2e576b5cc3ee3d67d78df8de83096dba325082107
Available editions
Research details
- Subjects
- Mathematics · Coding Theory
- Keywords
- average-radius list recovery, linear codes, folded Reed–Solomon codes, independent affine squares, two-fiber certificates
- Manuscript date
- 2026-10-19
- Reader reuse
- No additional permission granted
Scope
Linear codes over finite fields, binary input lists, independent-square profiles, and standard full-length folded Reed–Solomon realizations.
Reproduction
The downloadable package includes the manuscript, LaTeX source, three certificates, standard-library reproduction scripts, and saved verification receipts.
Publication package corrected to contain publication materials only. The manuscript and edition are unchanged.