A note on a gap in the proof of the minimum distance for Projective Reed-Muller Codes

TL;DR

This paper addresses a previously identified gap in the proof of the minimum distance for Projective Reed-Muller Codes, clarifying and correcting the proof to ensure its validity.

Contribution

It provides a detailed explanation of the original proof and successfully closes the gap, strengthening the theoretical foundation of Projective Reed-Muller Codes.

Findings

The gap in the original proof has been identified and addressed.

The corrected proof confirms the minimum distance properties of Projective Reed-Muller Codes.

Clarification enhances the reliability of coding theory results related to these codes.

Abstract

The note clarifies a gap in the proof of the minimum distance for Projective Reed-Muller Codes. The gap was identified by S.Ghorpade and R.Ludhani in a recent article. Here the original thoughts are explained and the gap closed.