Error Detection Codes and Correction Codes(2)

• General Properties

  • Minimum distance, dmin, of a code C: for any two code words I and J in C,
    d(I, J) ³ dmin
    
  • A code provides t error correction plus detection of s additional errors if and only if the following inequality is satisfied.
    2t + s + 1 £ dmin (1.25)
    
  • Example:
    • Single-error detection (SED): s = 1, t = 0, dmin = 2.
    • Single-error correction (SEC): s = 0, t = 1, dmin = 3.
    • Single-error correction and double-error detection (SEC and DED):
      s = t = 1, dmin = 4.
      

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