I have two vectors $a=[a_1, a_2,..a_n]$ and $b=[b_1,b_2,..b_n]$. A vector $c=[c_1...c_n]$ where $$c_i=\sum_{j=m}^l\alpha_j a_j+\sum_{j=k}^ h\beta_j b_j$$ In which, $i=1, \cdots, n; m,k \ge 1, m \le l \le n, k \le h \le n$ $\alpha_j$ and $\beta_j$ are coefficients in $\{0,1\}$. The above representing is to express a combination of random selecting elements in vector $a$ and $b$.
For example, $c_1=1.a_1+1.a_2+1.b_1; c_2=1.a_2; c_3=1.a_2+1.b_3, \cdots$
I want to represent above relationship of vector $c$ by using matrix. Could you suggest to me the matrix equation to represent it? Thank you
In my opinion, the vector $c$ maybe write as $$c= \begin{bmatrix} a&b \end{bmatrix}\cdot A_{1 \times 2n} $$ where $A \in GF(2)$ is a matrix $1 \times 2n$