Formalizing building-up constructions of self-dual codes through isotropic lines in Lean — Paper

Abstract

-cross Abstract: The purpose of this paper is two-fold. First, we show that, after a specified form isometry, the two-coordinate reduction in the binary Hilbert-symbol realization of Chinburg and Zhang is inverse to Kim's building-up construction, up to permutation equivalence. Second, for $q\equiv1\pmod4$, we develop a $q$-ary analogue of this reduction-and-extension mechanism. The identity $c^2=-1$ yields the isotropic line governing the split construction. For every fixed ordered pairing of the coordinates, we obtain a universal rank-$r$ boxed normal form, where $r$ is the dimension of the intersection with the product of these isotropic lines. Applications include optimal self-dual $[6,3,4]$ and $[8,4,4]$ codes over $\mathbb F_{5}$, optimal self-dual $[8,4,5]$ and $[10,5,6]$ codes over $\mathbb F_{13}$, and a self-dual $[12,6,6]$ code over $\mathbb F_{13}$. We also give an exact repeated boxed realization of self-dual $[18,9,8]$ and $[20,10,10]$ codes over $\mathbb F_{13}$, in which the split-boxed parent and its building-up child occur in one complete generator matrix. The algebraic core is formalized in Lean 4.

Authors 2

Jae-Hyun Baek, Jon-Lark Kim

Specification

Official page: arxiv.org/abs/2604.08485
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
arXiv id: 2604.08485
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Categories: cs.IT, cs.CL, math.IT
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
PDF: arxiv.org/pdf/2604.08485
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Primary category: cs.IT
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh

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9

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T19

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6 h ago

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None

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Authors: Jae-Hyun Baek, Jon-Lark Kim

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Claim history · Official page

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Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2604.08485	11 Sept 2026 21:03 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperFormalizing building-up constructions of self-dual codes through isotropic lines in Lean
New paper: Formalizing building-up constructions of self-dual codes through isotropic lines in Lean
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Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.CL	feed	T1· Official	4 h ago	1

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