Optical Coding Theory with Prime

1	Fundamental Materials and Tools

Modern algebra [1–5] provides mathematical concepts and tools fundamental to the study of Optical Coding Theory. The theory finds applications in coding-based optical systems and networks, for example, involving optical code-division multiple access (O-CDMA) and multiplexing [6–22]. Various families of the prime codes studied in this book are based on the arithmetic of finite or Galois fields of some prime numbers [1, 2, 21–23].

This chapter covers the essential concepts and algebraic tools that are useful for understanding the subject matter in this book. It begins with a review of Galois fields, followed by vector and matrix theories. Important code parameters, such as Hamming weight and distance, correlation ...