Plotkin Code
| Linear binary codes achieving Plotkin bound (maximum minimum distance) via recursive |
u |
u+v |
construction. Starting from [2,2,1] repetition code base, generates [2n, n+1, n] codes with optimal distance properties. Related to Hadamard matrices and first-order Reed-Muller codes. |
Properties
| Property |
Value |
| Category |
Error Correction |
| Sub-category |
Linear Code |
| Security status |
🎓 Educational Only |
| Complexity |
Intermediate |
| Inventor |
Morris Plotkin |
| Year |
1960 |
| Origin |
🇺🇸 United States |
| Source |
algorithms/ecc/plotkin-code.js |
Security
Status: 🎓 Educational Only
Known vulnerabilities
| Issue |
Description |
Mitigation |
| Power-of-2 Block Length |
Block length must be power of 2 (2, 4, 8, 16, …), limiting flexibility. |
— |
| Low Code Rate |
Code rate (n+1)/(2n) approaches 0.5 asymptotically, moderate efficiency. |
— |
Documentation
References
Test vectors
14 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Plotkin [2,2,1] base case - bits 00
| Field |
Value |
level |
0 |
input |
0000 |
expected |
0000 |
Vector 2 — Plotkin [2,2,1] base case - bits 01
| Field |
Value |
level |
0 |
input |
0001 |
expected |
0001 |
Vector 3 — Plotkin [2,2,1] base case - bits 10
| Field |
Value |
level |
0 |
input |
0100 |
expected |
0100 |
Vector 4 — Plotkin [2,2,1] base case - bits 11
| Field |
Value |
level |
0 |
input |
0101 |
expected |
0101 |
Vector 5 — Plotkin [4,3,2] level 1 - all zeros
| Field |
Value |
level |
1 |
input |
000000 |
expected |
00000000 |
Vector 6 — Plotkin [4,3,2] level 1 - pattern 001
| Field |
Value |
level |
1 |
input |
000001 |
expected |
00000100 |
Vector 7 — Plotkin [4,3,2] level 1 - pattern 010
| Field |
Value |
level |
1 |
input |
000100 |
expected |
00010001 |
Vector 8 — Plotkin [4,3,2] level 1 - pattern 011
| Field |
Value |
level |
1 |
input |
000101 |
expected |
00010101 |
Vector 9 — Plotkin [4,3,2] level 1 - pattern 100
| Field |
Value |
level |
1 |
input |
010000 |
expected |
01000100 |
Vector 10 — Plotkin [4,3,2] level 1 - all ones
| Field |
Value |
level |
1 |
input |
010101 |
expected |
01010001 |
Vector 11 — Plotkin [8,5,4] level 2 - all zeros
| Field |
Value |
level |
2 |
input |
0000000000 |
expected |
0000000000000000 |
Vector 12 — Plotkin [8,5,4] level 2 - pattern 00001
| Field |
Value |
level |
2 |
input |
0000000001 |
expected |
0000000000010001 |
Vector 13 — Plotkin [8,5,4] level 2 - pattern 10000
| Field |
Value |
level |
2 |
input |
0100000000 |
expected |
0100010001000100 |
Vector 14 — Plotkin [8,5,4] level 2 - all ones
| Field |
Value |
level |
2 |
input |
0101010101 |
expected |
0101000100000100 |
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