Keyun Cheng

Must-know erasure coding concepts for beginners

Finite Field

• field
  • operators: addition, multiplication
  • implementation: checkout Clemenson’s note on implementation of these two parameters
  • multiplication by checking log-table and log-inverse
  • fast multiplication on powers of 2
• prime
  • prime ideal
• polynomial
  • minimal polynomial
  • irreducible polynomial
  • generator polynomial
• conversion of a finite field to binary polynomials
  • differential equation
  • how to to find the irreducible polynomial
  • how the generator polynomial is constructed
• related codes
  • linear code
  • cyclic code
  • BCH code
  • Reed-Solomon code
  • bit-matrix code
  • array code

• systmatic code and non-systematic code construction

• online coding / offline coding