Neighbors, neighbor graphs and invariant rings in coding theory

2024/11/07 by Himadri Shekhar Chakraborty, Chakraborty, Himadri Shekhar, Williams Chiari +5
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Group Theory (math.GR) #Number Theory (math.NT) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2411.04647

openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we discuss the class of Type III and Type IV codes from the perspectives of neighbors. Our investigation analogously extends the results originally presented by Dougherty [8] concerning the neighbor graph of binary self-dual codes. Moreover, as an application of neighbors in invariant theory, we show that the ring of the weight enumerators of Type II code d_n⁺ and its neighbors in arbitrary genus is finitely generated. Finally, we obtain a minimal set of generators of this ring up to the space of degree 24 and genus 3.

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