FA-71965 / Error-correcting codes / Member archive

GF(256) multiply accumulates with integer addition · case 05

Products exceed 255 or differ from the field product.

Member previewVariant 5 · 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 [231, 130]	`465`	`45`	Failed

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