Galois hulls of cyclic serial codes over a finite chain ring

TL;DR

This paper investigates the properties of Galois hulls of cyclic serial codes over finite chain rings, introduces an algorithm for parameter computation, and analyzes the average Euclidean hull dimension and its growth.

Contribution

It provides new insights into Galois hulls of cyclic serial codes over chain rings and presents an algorithm for parameter determination.

Findings

Algorithm for computing Euclidean hull parameters

Average p^r-dimension of Euclidean hulls established

Results on the growth of hull dimensions

Abstract

In this paper, we explore some properties of Galois hulls of cyclic serial codes over a chain ring and we devise an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average $p^r$-dimension of the Euclidean hull, where $\mathbb{F}_{p^r}$ is the residue field of $R$, and we provide some results of its relative growth.