Hamming Distance Calculator
Hamming Distance: -
Understanding Hamming Distance
What is Hamming Distance?
Hamming distance is the number of positions at which corresponding symbols in two strings of equal length differ.
Properties:
- Non-negative: d(x,y) ≥ 0
- Identity: d(x,x) = 0
- Symmetry: d(x,y) = d(y,x)
- Triangle Inequality: d(x,z) ≤ d(x,y) + d(y,z)
Applications and Uses
- Error Detection
- Parity Checking
- Checksums
- CRC Codes
- Error Correction
- Hamming Codes
- Reed-Solomon Codes
- BCH Codes
- Information Theory
- Channel Coding
- Source Coding
- Data Compression
- Bioinformatics
- DNA Sequence Analysis
- Mutation Detection
- Sequence Alignment
Advanced Concepts
Minimum Distance
Error detection capability
Perfect Codes
Optimal error correction
Weight Distribution
Code performance analysis
Syndrome Decoding
Efficient error correction