ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book explains various families of the prime codes, which are based on the arithmetic of finite or Galois fields of some prime numbers. It describes optical coding theory with emphasis on prime codes, which are mainly incoherent codes. The term optical codes generally refers to this kind of code, which does not require phase tracking or system-wise synchronization, unless stated otherwise. Optical coding theory relies on modern algebra, which uses a different arithmetic system, rather than the familiar real and complex number systems. The concept of vector space over a finite field under modulo addition and multiplication is of particular interest in optical coding theory because one-dimensional optical codes can be represented as vectors over a finite field. Optical codes are traditionally designed with the cross-correlation functions as close to zero as possible for minimizing mutual interference.
