Error-Correction Coding Using Polynomial Residue Number System

There has been a tendency to use the theory of finite Galois fields, or GF(2n), in cryptographic ciphers (AES, Kuznyechik) and digital signal processing (DSP) systems. It is advisable modular codes polynomial residue number system (PRNS). Modular PRNS are arithmetic which addition, subtraction multiplication operations performed parallel on bases code, irreducible polynomials. In this case, operands small-bit residues. However, independence calculations code lack data exchange between residues can serve as basis for constructing capable detecting correcting errors that occur during calculations. The article will consider principles redundant system. results study with minimal redundancy presented. shown these only able detect an error combination PRNS. proposed two control bases, allows us correct any combination, order increase error-correction abilities Therefore, development algorithm system, performing procedure based effectively implemented PRNS, urgent task.