Binary codes from uniform subset graph G(n, 4, i)

Document Type : Full Length Article

Authors

1 Department of Mathematics, University of Zanjan Zanjan, Iran.

2 Department of Mathematics,University of Zanjan, Zanjan, Iran

Abstract

Let Ω be a set of cardinality n with n ≥ 8, and let V = P4(Ω) denote the family of all 4-element subsets of Ω. For i = 0, 1, 2, 3, let G(n,4,i) be the graph with vertex set V, where two vertices are adjacent precisely when their intersection has cardinality i. This graph is referred to as the uniform subset graph. We denote the adjacency matrix of G(n,4,i) by Ai(n). In this work, we investigate the binary codes Ci(n) arising from the row space of Ai(n), determine their parameters, and establish the relationships between Ci(n) and Cj(n)⊥ for i,j ∈ {0,1,2,3}.

Graphical Abstract

Binary codes from uniform subset graph G(n, 4, i)

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References

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Journal of Discrete Mathematics and Its Applications
Volume 11, Issue 3
September 2026
Pages 235-246

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History

  • Receive Date: 17 December 2025
  • Revise Date: 05 August 2026
  • Accept Date: 14 August 2026
  • First Publish Date: 30 August 2026
  • Publish Date: 01 September 2026

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