Representations of code loops by binary codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917184890994688 |
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| author | Pires, Rosemary Miguel Grishkov, Alexandre Rasskazova, Marina |
| author_facet | Pires, Rosemary Miguel Grishkov, Alexandre Rasskazova, Marina |
| contents | 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 $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representations of code loops by binary codes Pires, Rosemary Miguel Grishkov, Alexandre Rasskazova, Marina Group Theory 20N05 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 $4$. |
| title | Representations of code loops by binary codes |
| topic | Group Theory 20N05 |
| url | https://arxiv.org/abs/2601.02332 |