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arXiv · 2601.02332

Representations of code loops by binary codes

Rosemary Miguel Pires·Alexandre Grishkov·Marina Rasskazova
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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 $4$.

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Rosemary Miguel Pires, Alexandre Grishkov, Marina Rasskazova. 2026-01-05. Representations of code loops by binary codes. https://arxiv.org/abs/2601.02332

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