Formalizing building-up constructions of self-dual codes through isotropic lines in Lean
Updated 6 h ago · first seen 11 Sept 2026
paper_01M294G6HP72YT2K8YT8DQE062
- Published
- 11 Sept 2026
- T1 · 6 h ago
- arXiv
- 2604.08485
- T1 · 6 h ago
- Category
- cs.IT
- T1 · 6 h ago
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
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
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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Provenance
Attributed facts
9
Source tiers
T19
Freshest observation
6 h ago
Conflicts
None
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- Authors
- Jae-Hyun Baek, Jon-Lark Kim
As of
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Claim history
Official pageofficial_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/abs/2604.08485 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| -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. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Arxiv announce typearxiv_announce_type1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| replace | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
arXiv idarxiv_id1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 2604.08485 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Categoriescategories1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.IT, cs.CL, math.IT | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
PDFpdf_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/pdf/2604.08485 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Primary categoryprimary_category1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.IT | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Publishedpublished_at1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 11 Sept 2026 | → 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 →
- 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
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.CL | feed | T1· Official | 5 h ago | 1 |
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