Locally Testable Codes
Codes whose membership can be checked from local views, and the neighbouring notions of conflict checkability and local-to-global consistency.
| Status | Problem | Tags |
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Conflict Checkable Codes Beyond Half-Singleton Theorem 1.8 proves \(k\le(n-d+2)/2\) for codes that are both comparison-based and local-to-global consistent. Theorem 1.3 gives an almost-MDS conflict checkable code at \(k\ge n-d+1-\varepsilon\) which bypasses that bound, but it is neither comparison-based nor known to be local-to-global consistent. The conjecture names comparison-basedness as the culprit. It already holds at \(d=n-1\). 4 open |
Code Based CryptographyLocally Testable CodesThreshold Secret Sharingseparationadaptation (ai) |
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