FA-71999 / Error-correcting codes / Member archive

RS syndromes start at alpha to the first power · case 04

Codewords generated with roots alpha^0, alpha^1 fail the check.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Reed-Solomon syndromes over GF(2^8) (0x11D, alpha = 2, first consecutive root alpha^0). msg lists coefficients from the highest degree down. S_j = msg(alpha^j) for j = 0..nsym-1 by Horner evaluation. Return [syndromes, whether any syndrome is nonzero].

Why this case matters

Storage and broadcast decoders start every Reed-Solomon block with a syndrome check.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [[131, 154, 183, 135, 93, 251, 102, 233], 2]	`[[0, 199], true]`	`[[0, 0], false]`	Failed

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