A new reducibility results for minihypers in finite projective geometries

TL;DR

This paper introduces a new reducibility theorem for mini-hypers in finite projective geometries, enabling the characterization of specific minihypers and contributing to the understanding of ternary Griesmer codes.

Contribution

It presents a novel reducibility result for mini-hypers and applies it to characterize minihypers with parameters (70, 22) in PG(4, 3).

Findings

Characterization of minihypers with parameters (70, 22) in PG(4, 3)

New reducibility theorem for mini-hypers in finite projective geometries

Implications for the existence of certain ternary Griesmer codes

Abstract

In this paper we prove a new reducibility result for mini-hypers in projective geometries over finite fields. It is further used to characterize the minihypers with parameters (70, 22) in PG(4, 3). The latter can be used to attack the existence problem for some hypothetical ternary Griesmer codes of dimension 6.