First asymptotically good codes with constant rate, constant relative distance, and constant alphabet size. Constructed by concatenating Reed-Solomon outer code with Wozencraft ensemble inner codes. Discovered by Jørn Justesen in 1972. Used to prove existence of codes meeting Gilbert-Varshamov bound.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Concatenated Code |
| Security status | 🎓 Educational Only |
| Complexity | Expert |
| Inventor | Jørn Justesen |
| Year | 1972 |
| Origin | Not specified |
| Source | algorithms/ecc/justesen-code.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Decoding Complexity | Concatenated structure requires two-stage decoding (outer RS + inner Wozencraft). | — |
| Alphabet Size | Binary codes derived from larger alphabet, affecting practical implementation. | — |
4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Justesen code all zeros
| Field | Value |
|---|---|
input |
00000000 |
expected |
0000000000000000 |
Vector 2 — Justesen code pattern 1000
| Field | Value |
|---|---|
input |
01000000 |
expected |
0100010000000000 |
Vector 3 — Justesen code pattern 0100
| Field | Value |
|---|---|
input |
00010000 |
expected |
0001000100000000 |
Vector 4 — Justesen code pattern 1100
| Field | Value |
|---|---|
input |
01010000 |
expected |
0101010100000000 |