What is a Coding?

The word of the "coding" is one of the most widespread in modern computer science. What means the concept of the "coding"? The "coding" is perceived as the operation of the identification of the symbols or the symbol groups of one code to the symbols or the symbol groups of other code. The necessity of the "coding" arises first of all from need to adapt the form of message to the given "communication channel" or to some device intended for transformation, conversion or storage of information.

The Coding Theory has a long history The number systems intended for number representation were the first codes. The next very old direction of the coding theory is the cryptography or secret coding. This one takes its origin in the Egyptian science dating back almost 4000 years ago, to the time when the Egyptians used the hieroglyphic code for inscriptions on the tombs. Development of the modern coding theory was stimulated by the progress of the communication systems. Shannon's information theory based on the entropy concept is mathematical justification of the effective code theory. The Morse, Shannon-Fano and Haffman codes are the examples of the effective codes.

The needs to protect information and communication systems from noise stimulated the progress of the redundant codes theory. The Hamming and cyclic codes are well-known examples of the redundant codes.

    Thus the modern coding theory is a totality at least of the 4 different directions:
  1. number system theory;
  2. cryptography methods;
  3. effective codes theory;
  4. redundant codes theory.

The different mathematical theories are used widely for solution of the coding problems. For example, the group theory is used widely in the theory of algebraic codes, the number theory is the basis of modern cryptography.

However in the last years the matrix theory is used for development of the coding theory. And to understand the sense of the new coding theory based on Fibonacci matrices, it is necessary to study some initial concepts of the matrix theory. And we will tell about these concepts at the next page of our Museum. Follow us!