Maximum Distance Separable code achieving Singleton bound d=n-k+1 using Cauchy matrix construction. Provides optimal erasure correction with any k symbols sufficient to reconstruct message. Used in RAID-6, distributed storage, and network coding. Educational implementation demonstrating MDS property beyond Reed-Solomon.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Maximum Distance Separable Code |
| Security status | 🎓 Educational Only |
| Complexity | Advanced |
| Inventor | Richard Singleton |
| Year | 1964 |
| Origin | 🇺🇸 United States |
| Source | algorithms/ecc/singleton-bound-code.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Erasure-Only Correction | This implementation focuses on erasure correction (known error locations). Error correction requires syndrome decoding. | — |
| Galois Field Arithmetic Complexity | GF(256) operations require careful implementation. Performance depends on log/antilog table efficiency. | — |
| Matrix Inversion Numerical Stability | Cauchy matrix inversion over finite fields requires exact arithmetic to avoid reconstruction failures. | — |
5 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — MDS (6,4) encoding - systematic form with Cauchy parity
| Field | Value |
|---|---|
input |
01020304 |
expected |
010203041400 |
Vector 2 — MDS zero codeword test - demonstrates linearity
| Field | Value |
|---|---|
input |
00000000 |
expected |
000000000000 |
Vector 3 — MDS maximum value test in GF(256)
| Field | Value |
|---|---|
input |
ffffffff |
expected |
ffffffff6161 |
Vector 4 — MDS basis vector e_1 - first column of generator
| Field | Value |
|---|---|
input |
01000000 |
expected |
010000008ef4 |
Vector 5 — MDS random message - demonstrates general encoding
| Field | Value |
|---|---|
input |
64c83296 |
expected |
64c832962db0 |