FA-72288 / Error-correcting codes / Member archive

Weight distribution skips the zero message · case 03

The histogram totals 2^k - 1 and weight 0 is missing.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Weight distribution of the binary linear code spanned by the rows of generator matrix G (rows may be dependent). Enumerate all 2^k messages including the zero message, form codewords as XOR combinations of rows, and histogram their Hamming weights (index 0..n). dmin is the smallest nonzero weight present (0 if the code is only the zero word). Return [histogram, dmin].

Why this case matters

Code designers use weight enumerators to estimate undetected-error probability and 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 [[[1, 1, 0, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 0, 1]]]	`[[1, 2, 4, 4, 2, 2], 1]`	`[[2, 2, 4, 4, 2, 2], 1]`	Failed

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