The Neighbor Graph of Self-Dual Codes Over Finite Fields

Esengül Saltürk

doi:10.47000/tjmcs.1681863

The Neighbor Graph of Self-Dual Codes Over Finite Fields

Abstract

We extend the neighbor construction of binary self-dual codes to codes over arbitrary finite fields. We show that the neighbor graph of self-dual codes over the fields of even characteristic is a connected, regular graph and we count vertices, edges and $s$-neighbors in the graph. When the length is a multiple of $4,$ we define the neighbor graph of Type II codes over the field of order $4$ and count the vertices and the edges in the graph. We describe two graphs for self-dual codes over the fields of odd characteristic according to the existence of the subcode generated by the all one-vector and we determine the parameters of the neighbor graph of ternary self-dual codes.

Keywords

References

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics), Applied Mathematics (Other)

Journal Section

Research Article

Authors

Esengül Saltürk ^*
0000-0003-1409-1102
Türkiye

Publication Date

December 30, 2025

Submission Date

April 22, 2025

Acceptance Date

July 28, 2025

Published in Issue

Year 2025 Volume: 17 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1681863

IZ

https://izlik.org/JA53BL97UR

Cite

RIS / Bibtex

APA

Saltürk, E. (2025). The Neighbor Graph of Self-Dual Codes Over Finite Fields. Turkish Journal of Mathematics and Computer Science, 17(2), 450-471. https://doi.org/10.47000/tjmcs.1681863

AMA

1.Saltürk E. The Neighbor Graph of Self-Dual Codes Over Finite Fields. TJMCS. 2025;17(2):450-471. doi:10.47000/tjmcs.1681863

Chicago

Saltürk, Esengül. 2025. “The Neighbor Graph of Self-Dual Codes Over Finite Fields”. Turkish Journal of Mathematics and Computer Science 17 (2): 450-71. https://doi.org/10.47000/tjmcs.1681863.

EndNote

Saltürk E (December 1, 2025) The Neighbor Graph of Self-Dual Codes Over Finite Fields. Turkish Journal of Mathematics and Computer Science 17 2 450–471.

IEEE

[1]E. Saltürk, “The Neighbor Graph of Self-Dual Codes Over Finite Fields”, TJMCS, vol. 17, no. 2, pp. 450–471, Dec. 2025, doi: 10.47000/tjmcs.1681863.

ISNAD

Saltürk, Esengül. “The Neighbor Graph of Self-Dual Codes Over Finite Fields”. Turkish Journal of Mathematics and Computer Science 17/2 (December 1, 2025): 450-471. https://doi.org/10.47000/tjmcs.1681863.

JAMA

1.Saltürk E. The Neighbor Graph of Self-Dual Codes Over Finite Fields. TJMCS. 2025;17:450–471.

MLA

Saltürk, Esengül. “The Neighbor Graph of Self-Dual Codes Over Finite Fields”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 2, Dec. 2025, pp. 450-71, doi:10.47000/tjmcs.1681863.

Vancouver

1.Esengül Saltürk. The Neighbor Graph of Self-Dual Codes Over Finite Fields. TJMCS. 2025 Dec. 1;17(2):450-71. doi:10.47000/tjmcs.1681863

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