Solution of the [72, 36,16] Problem

TL;DR

This paper proves the non-existence of certain binary codes with specific parameters using a computational approach implemented in Mathematica.

Contribution

It provides a computational proof that no Type II binary codes exist with parameters [72, 36, 16] or [96, 48, 20], resolving a longstanding question.

Findings

No Type II binary code with parameters [72, 36, 16] exists.

No Type II binary code with parameters [96, 48, 20] exists.

The proof is based on computational methods implemented in Mathematica.

Abstract

This is the TeX version of the {\it Mathematica} file used to prove there is no Type II binary code with parameters [72, 36, 16] or [96, 48, 20].