Hawkynt

Dual Hamming Code

Dual code of Hamming (7,4) yielding Simplex (7,3) code. Generator matrix of dual is parity-check matrix of original. All non-zero codewords have constant Hamming weight 4. Demonstrates duality principle: dual of [n,k,d] code is [n,n-k,d_perp]. Educational example of code duality.

Properties

Property	Value
Category	Error Correction
Sub-category	Dual Code
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Richard Hamming (original), Dual concept classical
Year	1950
Origin	🇺🇸 United States
Source	algorithms/ecc/dual-hamming.js

Security

Status: 🎓 Educational Only

Known vulnerabilities

Issue	Description	Mitigation
Lower Rate	Dual code has rate k/n where original has (n-k)/n. Hamming (7,4) rate 4/7 → Dual rate 3/7.	—
Different Properties	Dual may have different error correction capabilities than original code.	—

Documentation

• Wikipedia - Dual Code
• Error Correction Zoo
• Linear Code Duality

References

• Self-Dual Codes
• Hamming Code
• Code Theory Basics

Test vectors

4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Dual Hamming (7,3) all zeros

Field	Value
input	000000
expected	00000000000000

Vector 2 — Dual Hamming (7,3) pattern 001

Field	Value
input	000001
expected	00000001010101

Vector 3 — Dual Hamming (7,3) pattern 010

Field	Value
input	000100
expected	00010100000101

Vector 4 — Dual Hamming (7,3) pattern 100

Field	Value
input	010000
expected	01000100010001

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