# A binary encoding of spinors and applications

## TL;DR

This paper introduces a binary encoding scheme for spinors and Clifford algebra operations, enabling efficient computational implementations and explicit descriptions of complex algebraic structures like triality automorphisms.

## Contribution

It provides a novel binary coding method for spinors and Clifford multiplication, facilitating explicit calculations and representations of advanced Lie algebra structures.

## Key findings

- Binary code for spinors and Clifford multiplication developed
- Explicit descriptions of triality automorphism of Spin(8) provided
- Representations of Lie algebras spin(8), spin(7), and g2 constructed

## Abstract

We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of $Spin(8)$, explicit representations of the Lie algebras $\mathfrak{spin}(8)$, $\mathfrak{spin}(7)$ and $\mathfrak{g}_2$, etc.