Minimal binary codewords derived from the incidence-matrix approach

Boran Kim

doi:10.1007/s40314-025-03580-6

Minimal binary codewords derived from the incidence-matrix approach

Boran Kim

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

Abstract

Given a simple, connected graph G, let C denote the binary linear code whose generator matrix is obtained by appending the incidence matrix of G to the identity matrix. In this paper, we establish a bijection between minimal codewords in C and the non-equivalent walks in G. For several families of graphs, we determine the exact number of minimal codewords.

Original language	English
Article number	200
Journal	Computational and Applied Mathematics
Volume	45
Issue number	5
DOIs	https://doi.org/10.1007/s40314-025-03580-6
State	Published - Jun 2026

Keywords

Graphs
Linear codes
Minimal codewords

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10.1007/s40314-025-03580-6

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title = "Minimal binary codewords derived from the incidence-matrix approach",

abstract = "Given a simple, connected graph G, let C denote the binary linear code whose generator matrix is obtained by appending the incidence matrix of G to the identity matrix. In this paper, we establish a bijection between minimal codewords in C and the non-equivalent walks in G. For several families of graphs, we determine the exact number of minimal codewords.",

keywords = "Graphs, Linear codes, Minimal codewords",

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KW - Minimal codewords

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Minimal binary codewords derived from the incidence-matrix approach

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