Perfect binary (24,12,8) linear code that can correct up to 3 errors or detect up to 4 errors. One of only two non-trivial perfect binary codes. Used in Voyager spacecraft, satellite communications, and mobile radio.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Linear Code |
| Security status | 🎓 Educational Only |
| Complexity | Advanced |
| Inventor | Marcel J. E. Golay |
| Year | 1949 |
| Origin | 🇨🇭 Switzerland |
| Source | algorithms/ecc/extended-golay.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Limited Block Size | Fixed 12-bit message size may not be optimal for all applications. | — |
| Decoding Complexity | Full syndrome decoding requires lookup tables or complex algebraic operations. | — |
3 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Extended Golay all zeros
| Field | Value |
|---|---|
input |
000000000000000000000000 |
expected |
000000000000000000000000000000000000000000000000 |
Vector 2 — Extended Golay all ones
| Field | Value |
|---|---|
input |
010101010101010101010101 |
expected |
010101010101010101010101010101010101010101010101 |
Vector 3 — Extended Golay single bit
| Field | Value |
|---|---|
input |
010000000000000000000000 |
expected |
010000000000000000000000010100000001010100010001 |