FA-72122 / Error-correcting codes / Member archive

Code capability weighs errors like erasures · case 02

Patterns with errors are declared decodable beyond the code capability.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

Given a block code as a list of equal-length codewords (duplicates allowed but ignored; fewer than two distinct words or unequal lengths return None), compute the minimum Hamming distance d, the guaranteed correction capability t = floor((d-1)/2), detection capability d-1, and whether a pattern of the given errors and erasures is decodable (2*errors + erasures < d). Return [d, t, detect, decodable].

Why this case matters

Link and storage designers budget error and erasure correction from the minimum distance.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression [[[0, 0, 0], [1, 1, 1]], 1, 1]	`[3, 1, 2, true]`	`[3, 1, 2, false]`	Failed

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