A partition of the hypercube into maximally nonparallel Hamming codes

TL;DR

This paper presents a novel method to partition the hypercube into Hamming code cosets with maximally nonparallel properties, enhancing code design by minimizing intersections.

Contribution

It introduces a construction using the Gold map to create hypercube partitions into Hamming codes with minimal intersections, a new approach in coding theory.

Findings

Constructed hypercube partitions with maximally nonparallel Hamming codes

Achieved minimal intersection cardinality between code cosets

Demonstrated the effectiveness of the Gold map in code partitioning

Abstract

By using the Gold map, we construct a partition of the hypercube into cosets of Hamming codes such that for every two cosets the corresponding Hamming codes are maximally nonparallel, that is, their intersection cardinality is as small as possible to admit nonintersecting cosets.