On the extention of propelinear structures of Nordstrom-Robinson code to Hamming code

TL;DR

This paper classifies propelinear structures on the Nordstrom-Robinson code and explores how these structures can be extended to the Hamming code containing it, using Fano plane representations.

Contribution

It provides a classification of propelinear structures on the Nordstrom-Robinson code and investigates their extension to the Hamming code, introducing a novel geometric approach.

Findings

Classification of propelinear structures on Nordstrom-Robinson code

Partial extension of these structures to Hamming code

Representation of partitions via Fano planes

Abstract

A code is called propelinear if its automorphism group contains a subgroup that acts regularly on its codewords, which is called a propelinear structure on the code. In the paper a classification of the propelinear structures on the Nordstrom-Robinson code is obtained and the question of extension of these structures to propelinear structures of the Hamming code, that contains the Nordstrom-Robinson code. The result partially relies on a representation of all partitions of the Hamming code into codes with parameters of Nordstrom-Robinson code via Fano planes which is given in the paper.