Weighted-Hamming Metric: Bounds and Codes
Information Theory
2026-01-21 v1 math.IT
Abstract
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of importance or noise. From a coding-theoretic perspective, the actual error-correction capability of a code under this metric can exceed half its minimum distance. In this work, we establish direct bounds on this capability, tightening those obtained via minimum-distance arguments. We also propose a flexible code construction based on generalized concatenation and show that these codes can be efficiently decoded up to a lower bound on the error-correction capability.
Cite
@article{arxiv.2601.12998,
title = {Weighted-Hamming Metric: Bounds and Codes},
author = {Sebastian Bitzer and Alberto Ravagnani and Violetta Weger},
journal= {arXiv preprint arXiv:2601.12998},
year = {2026}
}