Year: 2024
Type: article
Abstract: The first linear programming bound is the best known asymptotic upper bound for binary codes, for a certain subrange of distances. Starting from the work of Friedman and Tillich (2005), there are, by now, some arguably easier and more direct arguments for this bound. We show that this more recent line of argument runs into certain difficulties if one tries to go beyond this bound [say, towards the second linear programming bound of McEliece et al. (1977)]. Stated more constructively, we show that certain necessary requirements have to be met in order to produce a feasible solution to the dual linear program of Delsarte (1973), which improves on the first linear programming bound, following this line of argument.
Author: Alex Samorodnitsky
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G5549392536
OpenAlex ID: W4404577094