A Note on Non-Interactive Key Exchange from Code Equivalence

The authors propose to split the action of the monomial matrix into two parts, where only the evenor odd-numbered columns are affected. To do this, they define the sets EMn(q) and OMn(q), which are the subgroups of Monon(q) containing matrices that have a 1 in the odd-numbered and even-numbered elements of the diagonal, respectively. The set sub −Mn(q) is then defined as their union, and leads to the following problem.