Appendix F / F.3

F.3 RELEVANCE TO CODING THEORY

Galois Fields provide a closed algebraic structure suitable for discrete symbol manipulation. Binary linear block codes, BCH codes, and Reed–Solomon codes are all defined over Galois Fields of the form GF(2^m), where each element represents an m-bit symbol. In these extension fields, addition is performed modulo 2 (bitwise XOR), while multiplication is defined modulo an irreducible polynomial of degree m.