FA-72018 / Error-correcting codes / Member archive

RS single-error correction applies S1 as the magnitude · case 03

The located symbol is changed by the wrong amount.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Correct at most one symbol error in a Reed-Solomon codeword with two parity symbols over GF(2^8) (0x11D, roots alpha^0 and alpha^1, alpha = 2). msg lists coefficients highest degree first, so index n-1-i holds degree i. With S0 = msg(1) and S1 = msg(alpha): both zero -> clean; one zero -> uncorrectable; else the error degree is log(S1/S0), which must be < n, and the error value is S0. Return [corrected symbols or None, status].

Why this case matters

Short-block RS codes in barcodes and radio headers correct a single corrupted symbol cheaply.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [[29, 68, 82, 251, 193, 203, 215, 101]]	`[[29, 68, 82, 15, 193, 203, 215, 101], "corrected"]`	`[[29, 68, 82, 179, 193, 203, 215, 101], "corrected"]`	Failed

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