First-order Reed-Muller codes RM(1,m) with parameters [2^m, 1+m, 2^(m-1)]. Closely related to Hadamard codes and biorthogonal codes. Simple decoding using majority logic. Used in wireless communications and deep-space missions.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Linear Code |
| Security status | š Educational Only |
| Complexity | Advanced |
| Inventor | David E. Muller, Irving S. Reed |
| Year | 1954 |
| Origin | šŗšø United States |
| Source | algorithms/ecc/reed-muller.js |
Status: š Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Low Code Rate | First-order RM codes have low code rate (1+m)/2^m, decreasing with larger m. | ā |
| Fixed Block Lengths | Block length must be a power of 2, limiting flexibility. | ā |
3 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 ā RM(1,3) all zeros
| Field | Value |
|---|---|
input |
00000000 |
expected |
0000000000000000 |
Vector 2 ā RM(1,3) all ones
| Field | Value |
|---|---|
input |
01010101 |
expected |
0100000100010100 |
Vector 3 ā RM(1,3) pattern test
| Field | Value |
|---|---|
input |
01000000 |
expected |
0101010101010101 |