The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes
Information Theory
2024-05-01 v1 math.IT
Abstract
Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is static, the appropriate length can be obtained by an RS code by shortening or puncturing. Generalized Reed-Solomon (GRS) codes are a generalization of RS codes, whose subfield-subcodes are extensively studied. In this paper we show that a particular class of GRS codes produces many subfield-subcodes with large dimension. An algorithm for searching through the codes is presented as well as a list of new codes obtained from this method.
Keywords
Cite
@article{arxiv.1108.5475,
title = {The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes},
author = {Fernando Hernando and Kyle Marshall and Michael E. O'Sullivan},
journal= {arXiv preprint arXiv:1108.5475},
year = {2024}
}