On Binary Shadow Codes
Information Theory
2024-09-04 v3 math.IT
Abstract
We generalize the shadow codes of Cherubini and Micheli to include basic polynomials having arbitrary degree, and show that restricting basic polynomials to have degree one or less can result in improved lower bounds on the minimum distance of the code. However, even these improved lower bounds suggest that shadow codes have considerably inferior distance-rate characteristics compared with the concatenation of a Reed-Solomon outer code and a first-order Reed-Muller inner code.
Cite
@article{arxiv.2408.09287,
title = {On Binary Shadow Codes},
author = {Amir Tasbihi and Frank R. Kschischang},
journal= {arXiv preprint arXiv:2408.09287},
year = {2024}
}