Preprint Communication Version 2 Preserved in Portico This version is not peer-reviewed

# Complete Quantum Information in the DNA Genetic Code

Version 1 : Received: 17 July 2020 / Approved: 17 July 2020 / Online: 17 July 2020 (16:20:35 CEST)
Version 2 : Received: 5 October 2020 / Approved: 6 October 2020 / Online: 6 October 2020 (10:11:17 CEST)

How to cite: Planat, M.; Aschheim, R.; Amaral, M.; Fang, F.; Irwin, K. Complete Quantum Information in the DNA Genetic Code. Preprints 2020, 2020070403 (doi: 10.20944/preprints202007.0403.v2). Planat, M.; Aschheim, R.; Amaral, M.; Fang, F.; Irwin, K. Complete Quantum Information in the DNA Genetic Code. Preprints 2020, 2020070403 (doi: 10.20944/preprints202007.0403.v2).

## Abstract

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature $G=\mathbb{Z}_5 \rtimes H$ where $H=\mathbb{Z}_2 . S_4\cong 2O$ is isomorphic to the binary octahedral group $2O$ and $S_4$ is the symmetric group on four letters/bases. The second group has signature $G=\mathbb{Z}_5 \rtimes GL(2,3)$ and points out a threefold symmetry of base pairings. For those groups, the representations for the $22$ conjugacy classes of $G$ are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the $22$ characters of $G$ attached to those representations are informationally complete. The biological meaning of these coincidences is discussed.

## Subject Areas

DNA genetic code; informationally complete characters; finite groups,; hyperelliptic curve

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