Finite Field Arithmetic for Network Coding
Muriel Médard, Vipindev Adat Vasudevan, Morten Videbæk Pedersen, Ken R. Duffy · 2025
Network coding considers nodes in a network operating on the data flows traversing them. The arithmetic operations used in such cases are defined within a branch of mathematics known as finite fields or Galois fields. Finite field arithmetic is used when performing the three core operations in network coding, namely: encoding, recoding, and decoding. This chapter demystifies finite field arithmetic by providing a detailed discussion on how it is performed for efficient network coding operations. Both algorithms and concepts are presented. By the end of the chapter, you should be able to understand how different arithmetic operations, particularly multiplication and division, are performed in finite fields and extension fields, as well as techniques to quickly performthem.