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Extended Self-Dual Code

Extended Hamming [8,4,4] code that is self-dual (C = C⊥). Type II doubly-even self-dual code where all codewords have weight divisible by 4. Generator matrix equals parity-check matrix. Educational example of self-duality. Can correct 1-bit error and detect 2-bit errors (SECDED).

Properties

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

Security

Status: 🎓 Educational Only

Known vulnerabilities

Issue	Description	Mitigation
Fixed Parameters	Self-dual property requires n even and k=n/2, limiting code parameters.	—
Limited Correction	Extended Hamming [8,4,4] can only correct single-bit errors.	—

Documentation

• Wikipedia - Self-Dual Code
• Error Correction Zoo
• Extended Hamming

References

• Type II Codes
• Self-Dual Construction
• Doubly-Even Codes

Test vectors

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

Vector 1 — Extended Self-Dual [8,4] all zeros

Field	Value
input	00000000
expected	0000000000000000

Vector 2 — Extended Self-Dual [8,4] pattern 1000

Field	Value
input	01000000
expected	0100000001010001

Vector 3 — Extended Self-Dual [8,4] pattern 0100

Field	Value
input	00010000
expected	0001000001000101

Vector 4 — Extended Self-Dual [8,4] all ones

Field	Value
input	01010101
expected	0101010101010101

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