The Neighbor Graph of Self-Dual Codes Over Finite Fields

Year 2025, Volume: 17 Issue: 2, 450 - 471, 30.12.2025

Esengül Saltürk

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

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

Self-dual codes , Graph , Neighbor code , Finite fields

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