Varshamov Code

Systematic code with dynamic r and k calculation.

📚 About Algorithm

Varshamov code is built based on a given length n and minimum distance d. The number of parity bits r is found using an inequality, and t errors are corrected via syndromes.

  • Calculation: G matrix rows k = n - r, where r is found via 2^r > 1 + Σ C(n-1, i).
  • Correction: The syndrome points to a specific column in the parity-check matrix H corresponding to the error position.
Generator Matrix G (k × n)
Parity Matrix H (r × n)
Input Data (U)
Code Word (V)