ON THE SYSTEMATIC ENCODING OF P-ARY REED-SOLOMON CODES WITH AN ARBITRARY PRIME P

Authors

  • Zhaneta Savova Computer Systems and Technologies Department, Faculty of Artillery, Air Defense and Communication and Information Systems, National Military University (BG)
  • Antoniya Tasheva Computer Systems Department, Faculty of Computer Systems and Technologies, Technical University of Sofia (BG)
  • Rosen Bogdanov Communication Networks and Systems Department, Faculty of Artillery, Air Defense and Communication and Information Systems, National Military University (BG)

DOI:

https://doi.org/10.17770/etr2025vol2.8568

Keywords:

Reed-Solomon Codes, Systematic Encoding, LFSR-based pRS Encoder, Multilevel Sequences, PAM-3, PAM-5

Abstract

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.

Supporting Agencies
The article was prepared with the financial support of the National Scientific Program “Security and Defence”, funded by the Ministry of Education and Science of the Republic of Bulgaria, in implementation of Decision № 731 of 21.10.2021 of the Council of Ministers of the Republic of Bulgaria.

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Published

08.06.2025

Issue

Vol. 2 (2025): Environment. Technology. Resources. Proceedings of the 16th International Scientific and Practical Conference. Volume 2

Section

Information Technologies

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Copyright (c) 2025 Zhaneta Savova, Antoniya Tasheva, Rosen Bogdanov

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Z. Savova, A. Tasheva, and R. Bogdanov, “ON THE SYSTEMATIC ENCODING OF P-ARY REED-SOLOMON CODES WITH AN ARBITRARY PRIME P”, ETR, vol. 2, pp. 299–306, Jun. 2025, doi: 10.17770/etr2025vol2.8568.