Encoding with (15,9) Reed-Solomon Codes over GF(24): A Focused Study on the Encoding Process
Adriana Naydenova Borodzhieva, Snezhinka Lubomirova Zaharieva, Dimitar N. Stoyanov · 2025
The paper describes the process of encoding a message using (15, 9) Reed-Solomon code, based on the Galois field GF(24), generated by one of the fourth-degree primitive irreducible polynomials$f(x)=x^4+x+1$. A detailed explanation for constructing the generator polynomial of the Reed-Solomon code is given in the paper. This code is capable of detecting and correcting errors occurring in three symbols of the codeword. The process of encoding a 36-bit information word is illustrated. The material is used in the optional course “Coding in Telecommunication Systems”, included in the curriculum of the “Internet and Mobile Communications” major for the Bachelor's degree.