Optimal codes and arcs for the generalized Hamming weights
Combinatorics
2026-01-05 v1 Information Theory
math.IT
Abstract
This text contains some notes on the Griesmer bound. In particular, we give a geometric proof of the Griesmer bound for the generalized weights and show that a Solomon--Stiffler type construction attains it if the minimum distance is sufficiently large. We also determine the parameters of optimal binary codes for dimensions at most seven and the optimal ternary codes for dimensions at most five.
Cite
@article{arxiv.2601.00250,
title = {Optimal codes and arcs for the generalized Hamming weights},
author = {Sascha Kurz and Ivan Landjev and Assia Rousseva},
journal= {arXiv preprint arXiv:2601.00250},
year = {2026}
}
Comments
27 pages and 8 tables; comments very welcome. arXiv admin note: substantial text overlap with arXiv:2412.14615