Set of linear codes where most codes satisfy Gilbert-Varshamov bound. Named after John Wozencraft. Used as inner codes in Justesen code construction. Ensemble consists of all [n,k] linear codes generated by random generator matrices. With high probability, randomly chosen code from ensemble is good.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Linear Code |
| Security status | 🎓 Educational Only |
| Complexity | Expert |
| Inventor | John Wozencraft |
| Year | 1960 |
| Origin | 🇺🇸 United States |
| Source | algorithms/ecc/wozencraft-ensemble.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Random Construction | Requires random sampling of generator matrices - no explicit construction. | — |
| Probabilistic Guarantee | Good properties hold with high probability, not deterministically for all codes. | — |
4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Wozencraft [4,2] all zeros
| Field | Value |
|---|---|
input |
0000 |
expected |
00000000 |
Vector 2 — Wozencraft [4,2] pattern 10
| Field | Value |
|---|---|
input |
0100 |
expected |
01000101 |
Vector 3 — Wozencraft [4,2] pattern 01
| Field | Value |
|---|---|
input |
0001 |
expected |
00010100 |
Vector 4 — Wozencraft [4,2] pattern 11
| Field | Value |
|---|---|
input |
0101 |
expected |
01010001 |