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