On the minimum distance graph of an extended Preparata code

TL;DR

This paper investigates the structure of the minimum distance graph of extended Preparata codes, establishing that isomorphism of these graphs implies code equivalence, thus linking graph properties to code classification.

Contribution

It proves that the minimum distance graphs of extended Preparata codes are isomorphic if and only if the codes are equivalent, providing a new criterion for code equivalence.

Findings

Minimum distance graphs are characterized by their clique structures.

Graph isomorphism corresponds to code equivalence for extended Preparata codes.

The paper establishes a necessary and sufficient condition for code equivalence based on graph isomorphism.

Abstract

The minimum distance graph of an extended Preparata code P(m) has vertices corresponding to codewords and edges corresponding to pairs of codewords that are distance 6 apart. The clique structure of this graph is investigated and it is established that the minimum distance graphs of two extended Preparata codes are isomorphic if and only if the codes are equivalent.