Subfield-Subcodes of Generalized Toric codes
Fernando Hernando, Michael E. O'Sullivan, Emanuel Popovici and, Shraddha Srivastava
TL;DR
This paper investigates subfield-subcodes of Generalized Toric codes over finite fields, providing polynomial generators, bounds on minimum distance, and examples of optimal codes over binary and ternary fields.
Contribution
It introduces polynomial generators for subfield-subcodes of GT codes, enabling dimension calculation and minimum distance bounds, with practical examples of high-performance codes.
Findings
Polynomial generators for subfield-subcodes identified
Bounds for minimum distance established
Examples of best known binary and ternary codes provided
Abstract
We study subfield-subcodes of Generalized Toric (GT) codes over . These are the multidimensional analogues of BCH codes, which may be seen as subfield-subcodes of generalized Reed-Solomon codes. We identify polynomial generators for subfield-subcodes of GT codes which allows us to determine the dimensions and obtain bounds for the minimum distance. We give several examples of binary and ternary subfield-subcodes of GT codes that are the best known codes of a given dimension and length.
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