FA-71958 / Error-correcting codes / Member archive

GF(256) multiply reduces with the AES polynomial · case 03

Products that overflow the byte disagree with the Reed-Solomon field.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Multiply two elements of GF(2^8) defined by the primitive polynomial x^8+x^4+x^3+x^2+1 (0x11D) using shift-and-add. Operands outside 0..255 return None.

Why this case matters

Reed-Solomon codecs for storage and QR codes are built on GF(2^8) arithmetic with polynomial 0x11D.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [243, 34]	`180`	`240`	Failed

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