ON THE SYSTEMATIC ENCODING OF P-ARY REED-SOLOMON CODES WITH AN ARBITRARY PRIME P (ENVIRONMENT. TECHNOLOGY. RESOURCES. Proceedings of the International Scientific and Practical Conference, 2025)
The Reed-Solomon (RS) codes, which are a subset of error-correcting codes, are currently employed in a number of significant applications. The most notable of these are data recovery in storage systems, barcodes in management and advertising systems, and communication systems and networks. In the present technological era, RS codes over Galois fields GF(2m) are frequently employed in the aforementioned applications, with GF(28) being the most prevalent. This enables the representation of all 256 values of a byte as a polynomial with eight binary coefficients over GF(28). The motivation for verifying and generalizing the idea of systematic encoding of RS codes in a field with a base p other than 2 stems from the fact that the mathematical dependencies in arbitrary field GF(pm) are not only valid for GF(2m), but also have wider applicability. Consequently, the article establishes the specific features of the systematic encoding of p-ary Reed-Solomon codes and LFSR-based systematic encoder, conceptualizing them as a class of cyclic codes over any field GF(pm) whose base is a prime p other than 2.