Nonlinear (16, 256, 6) code achieving optimal parameters. Has minimum distance 6, can correct 2 errors and detect 5 errors. Meets the Plotkin bound for binary codes. Notable as the best-known nonlinear code of length 16. Used in theoretical coding research.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Nonlinear Code |
| Security status | 🎓 Educational Only |
| Complexity | Expert |
| Inventor | A. W. Nordstrom, J. P. Robinson |
| Year | 1967 |
| Origin | 🇺🇸 United States |
| Source | algorithms/ecc/nordstrom-robinson.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Nonlinear Complexity | Nonlinear structure makes encoding/decoding more complex than linear codes. | — |
| Fixed Length | Only defined for length 16, cannot be easily extended to other lengths. | — |
4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Nordstrom-Robinson all zeros
| Field | Value |
|---|---|
input |
0000000000000000 |
expected |
00000000000000000000000000000000 |
Vector 2 — Nordstrom-Robinson pattern 1
| Field | Value |
|---|---|
input |
0000000000000001 |
expected |
01010101010101010101010101010101 |
Vector 3 — Nordstrom-Robinson pattern 2
| Field | Value |
|---|---|
input |
0000000100000000 |
expected |
00010001000100010001000100010001 |
Vector 4 — Nordstrom-Robinson pattern 3
| Field | Value |
|---|---|
input |
0100000000000000 |
expected |
00000000000000000101010101010101 |