Perfect [11,6,5] ternary linear code over GF(3) with 729 codewords. Can correct 2 ternary symbol errors. Minimum distance 5. One of only five perfect codes. Discovered by Marcel Golay in 1949. Used in quantum computing and magic state distillation. Quadratic residue code construction.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Perfect Code |
| Security status | 🎓 Educational Only |
| Complexity | Advanced |
| Inventor | Marcel J. E. Golay |
| Year | 1949 |
| Origin | 🇨🇭 Switzerland |
| Source | algorithms/ecc/ternary-golay.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Fixed Parameters | Only defined for [11,6,5] parameters, cannot be extended or shortened. | — |
| Ternary Alphabet | Requires ternary symbols (0,1,2) instead of binary, complicating hardware implementation. | — |
4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Ternary Golay all zeros
| Field | Value |
|---|---|
input |
000000000000 |
expected |
0000000000000000000000 |
Vector 2 — Ternary Golay pattern [1,0,0,0,0,0]
| Field | Value |
|---|---|
input |
010000000000 |
expected |
0100000000000101020201 |
Vector 3 — Ternary Golay pattern [0,1,0,0,0,0]
| Field | Value |
|---|---|
input |
000100000000 |
expected |
0001000000000102010102 |
Vector 4 — Ternary Golay pattern [2,1,0,0,0,0]
| Field | Value |
|---|---|
input |
020100000000 |
expected |
0201000000000001020201 |