Nonlinear binary code that is Z4-linear. For odd m, parameters [2^(m+1), 2^(2m), 2^m - 2^((m-1)/2)]. The [16, 256, 6] Kerdock code (m=3) achieves optimal nonlinear parameters. Related to Preparata codes via Gray map. Important in sequence design and wireless communications.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Nonlinear Code |
| Security status | 🎓 Educational Only |
| Complexity | Expert |
| Inventor | A. M. Kerdock |
| Year | 1972 |
| Origin | 🇺🇸 United States |
| Source | algorithms/ecc/kerdock-code.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Nonlinear Structure | Nonlinear codes have complex decoding, no simple syndrome decoding like linear codes. | — |
| Fixed Parameters | Kerdock codes only defined for specific parameter sets based on odd m. | — |
4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Kerdock [16,6] all zeros
| Field | Value |
|---|---|
m |
3 |
input |
000000000000 |
expected |
00000000000000000000000000000000 |
Vector 2 — Kerdock [16,6] pattern 100000
| Field | Value |
|---|---|
m |
3 |
input |
010000000000 |
expected |
00010001000100010001000100010001 |
Vector 3 — Kerdock [16,6] pattern 010000
| Field | Value |
|---|---|
m |
3 |
input |
000100000000 |
expected |
00000101000001010000010100000101 |
Vector 4 — Kerdock [16,6] pattern 001000
| Field | Value |
|---|---|
m |
3 |
input |
000001000000 |
expected |
00000000010101010000000001010101 |