They’re like Hamming codes, but this time with algebra (and alphas)

Single-Error BCH Codes

$C(X) = I(X) + R(X)$

$I(X) === R(X) mod M(X)$

  • $C(X)$ - Codeword
  • $I(X)$ - Information
  • $R(X)$ - Remainder
  • $M(X)$ - Minimal polynomial

The first $m$ ‘bits’ form the check bits, and the last $k$ form the information bits