When the extension property does not hold for vector space alphabets

TL;DR

This paper investigates the extension property for linear codes over vector space alphabets, providing new characterizations and improvements, especially focusing on the concept of G-pseudo-injectivity.

Contribution

It offers new insights and detailed descriptions of the extension property and G-pseudo-injectivity for vector space alphabets, advancing understanding beyond previous characterizations.

Findings

Improved characterization of the extension property for vector space alphabets

Detailed description of G-pseudo-injectivity in vector spaces

Identification of cases where the extension property does not hold

Abstract

In our recent paper we characterized the extension property for symmetrized weight composition for linear codes over a module alphabet. Several improvements for the case of vector space alphabets are given in this paper. A detailed description of the property of $G$-pseudo-injectivity for vector spaces is made.