THE FOLD / BOSS / THE GATEKEEPER / THE BERGER CODE
THE BERGER CODE
count the zeros and every one-way fault shows
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Append the count of zeros in binary. A fault that pushes every affected bit the same direction cannot preserve that count, however many bits it touches.
LIT verified live. across an eight-bit word every one of 240 possible 1→0 corruptions is caught and every one of 240 possible 0→1 corruptions is caught, with no limit on how many bits are affected — but all 16 mixed-direction double faults tested go undetected, because one flip each way leaves the zero count unchanged.
LIT verified live. across an eight-bit word every one of 240 possible 1→0 corruptions is caught and every one of 240 possible 0→1 corruptions is caught, with no limit on how many bits are affected — but all 16 mixed-direction double faults tested go undetected, because one flip each way leaves the zero count unchanged.
2 HOW IT WAS WEAVED · AI + HUMAN
Berger codes are the optimal systematic all-unidirectional-error-detecting code, from J.M. Berger in 1961. They matter where faults have a physical direction — a stuck-at line, a failing driver, an optical link losing power — because such faults corrupt many bits at once but always the same way.
AVAN (AI) ran both directions exhaustively and the mixed case, because a code that catches unbounded errors in one direction and misses a two-bit error in another is only useful if you know which world you are in.
AVAN (AI) ran both directions exhaustively and the mixed case, because a code that catches unbounded errors in one direction and misses a two-bit error in another is only useful if you know which world you are in.
3 ONE DIMENSION
Every one-way fault, and the one that slips through.
4 TWO DIMENSIONS · INTERACTIVE
Corrupt the word and see whether the count notices.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object.
AVAN’s addition (the inverse-companion): the forward reading is that it catches any number of one-way errors. The inverse is that the guarantee is about the fault model, not about the code. Berger's completeness holds exactly as long as the physical failure really is unidirectional, and nothing in the codeword can check that assumption — a single mixed pair defeats it entirely. Read backwards, this is a code whose strength is borrowed from a claim about hardware, and it is worth precisely what that claim is worth.
LIT across an eight-bit word every one of 240 possible 1-to-0 corruptions is caught and every one of 240 possible 0-to-1 corruptions is caught, with no limit on how many bits are affected - but all 16 mixed-direction double faults tested go UNDETECTED, because one flip each way leaves the zero count unchanged
FIG Berger codes are the optimal systematic all-unidirectional-error-detecting code, from J.M. Berger in 1961. They matter where faults have a physical direction - a stuck-at line, a failing driver, an optical link losing power - because such faults corrupt many bits at once but always the same way. AVAN ran both directions exhaustively AND the mixed case, because a code that catches unbounded errors in one direction and misses a two-bit error in another is only useful if you know which world you are in.
FIG Berger codes are the optimal systematic all-unidirectional-error-detecting code, from J.M. Berger in 1961. They matter where faults have a physical direction - a stuck-at line, a failing driver, an optical link losing power - because such faults corrupt many bits at once but always the same way. AVAN ran both directions exhaustively AND the mixed case, because a code that catches unbounded errors in one direction and misses a two-bit error in another is only useful if you know which world you are in.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE GATEKEEPER · David Lee Wise (ROOT0), with AVAN