Canonical Forms of $2\times 2\times 2$ and $2\times 2\times 2\times 2$ Symmetric Tensors over Prime Fields

We consider symmetric tensors of format $2\times 2\times 2$ and $2 \times 2 \times 2 \times 2$ over prime fields. Using computer algebra we compute the canonical forms of these tensors. For $2\times 2\times 2$ symmetric tensors, we consider the prime fields ${\mathbb{F}}_p$ for $p=2,3,5,7,11,13,17$. For $2\times 2\times 2\times 2$ symmetric tensors, we consider the prime fields ${\mathbb{F}}_p$ for $p=2,3,5,7$. For each canonical form, we determine the size of its orbit and the symmetric rank of the symmetric tensors in its orbit.