Representations of code loops by binary codes

Rosemary Miguel Pires; Alexandre Grishkov; Marina Rasskazova

Representations of code loops by binary codes

Group Theory 2026-01-06 v1

Authors: Rosemary Miguel Pires , Alexandre Grishkov , Marina Rasskazova

Abstract

Code loops are Moufang loops constructed from doubly even binary codes. Then, given a code loop $L$ , we ask which doubly even binary code $V$ produces $L$ . In this sense, $V$ is called a representation of $L$ . In this article we define and show how to determine all minimal and reduced representations of nonassociative code loops of rank $3$ and $4$ .

Keywords

coding theory combinatorial designs

Cite

@article{arxiv.2601.02332,
  title  = {Representations of code loops by binary codes},
  author = {Rosemary Miguel Pires and Alexandre Grishkov and Marina Rasskazova},
  journal= {arXiv preprint arXiv:2601.02332},
  year   = {2026}
}

Comments

30 pages, 19 figures. Revised and extended version of arXiv:1909.05143, following referee reports. Submitted to the International Journal of Algebra and Computation

Representations of code loops by binary codes

Abstract

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