I want to programmatically solve the following system (here in size 3): $$ \left\{ \begin{array}{ll} x_1 y_1 &\equiv a_1 \pmod 2 \\ x_2 y_1 + x_1 y_2 &\equiv a_2 \pmod 2 \\ x_3 y_1 + x_2 y_2 + x_1 y_3 &\equiv a_3 \pmod 2 \\ \qquad\quad\space x_3 y_2 + x_2 y_3 &\equiv a_4 \pmod 2 \\ \qquad\qquad\qquad\space\space x_3 y_3 &\equiv a_5 \pmod 2 \\ \end{array} \right. $$ I found those academic papers that seem to be in the field:
- http://www.mmrc.iss.ac.cn/pub/mm25.pdf/3.pdf
- http://www.mmrc.iss.ac.cn/~xgao/paper/csz2-0805.pdf
- https://link.springer.com/chapter/10.1007/978-3-319-61204-1_26
However, I'm having hard time understanding them (I'm a computer scientist). Would anyone explain how to tackle this kind of problem, or point me to an appropriate ressource? Thanks.