Bounds on $k$-hash distances and rates of linear codes

Stefano Della Fiore; Marco Dalai

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arXiv · 2505.05239

Bounds on $k$-hash distances and rates of linear codes

Stefano Della Fiore·Marco Dalai

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Abstract

In this paper, we bound the rate of linear codes in $\mathbb{F}_q^n$ with the property that any $k\leq q$ codewords are all simultaneously distinct in at least $d_k$ coordinates. For the case of particular interest $q=k=3$ we recover, with a simpler proof, state of the art results in the case $d_3=1$ and new bounds for $d_3>1$. We finally discuss some related open problems on the list-decoding zero-error capacity of discrete memoryless channels.

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Stefano Della Fiore, Marco Dalai. 2025-05-08. Bounds on $k$-hash distances and rates of linear codes. https://arxiv.org/abs/2505.05239

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