An upper bound on the size of a binary code with $$s$$ distances

Let $$C$$ be a binary code of length $$n$$ with distances $$0<d_1<\cdots<d_s\le n$$. In this note we prove a general upper bound on the size of $$C$$ without any restriction on the distances $$d_i$$. The bound is asymptotically optimal.

Authors

Konstantin Vorob’ev (ORCID: https://orcid.org/0000-0002-3808-9771)
Ivan Landjev (ORCID: https://orcid.org/0000-0001-5147-5186)

Institutions

Bulgarian Academy of Sciences (BG)

Publication Details

Journal: Proceedings of the Bulgarian Academy of Sciences
Published: 2025-05-28
DOI: https://doi.org/10.7546/crabs.2025.05.02
Primary Topic: Coding theory and cryptography
Type: article
Field-Weighted Citation Impact: 0.00

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article

An upper bound on the size of a binary code with $$s$$ distances

Konstantin Vorob’ev, Ivan Landjev

May 28, 2025

Proceedings of the Bulgarian Academy of Sciences

Coding theory and cryptography

article

An upper bound on the size of a binary code with $$s$$ distances

Konstantin Vorob’ev, Ivan Landjev

May 28, 2025article en

Abstract

Proceedings of the Bulgarian Academy of SciencesVol. 78(5)

Bulgarian Academy of Sciences (BG)

Openalex Percentile: Top 94%

Coding theory and cryptography

DOI Open Access PDF OpenAlex

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An upper bound on the size of a binary code with $s$ distances — Konstantin Vorob’ev, Ivan Landjev · Proceedings of the Bulgarian Academy of Sciences (2025) | TGRS Research Map | TGRS