FA-71980 / Error-correcting codes / Member archive

GF(256) antilog table is not extended · case 05

The inverse of 1 is reported as 0.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Table-driven GF(2^8) (polynomial 0x11D, generator 2) operations: "div" a/b (None for b = 0, 0 for a = 0 otherwise), "inv" 1/a (None for 0) and "pow" a^b for integer b >= 0 (0^0 = 1, 0^b = 0). EXP is extended to 510 entries so sums of logarithms need no reduction. Unknown ops return None.

Why this case matters

Reed-Solomon decoders spend most time in log/antilog table lookups for division and inversion.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression ["inv", 1, 0]	`0`	`1`	Failed

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