I. Introduction
An matrix is detecting if and only if $$Ax=Ay \quad \Longrightarrow \quad x=y \eqno{\hbox{(1)}}$$for . An equivalent definition is $$Ae=0 \quad \Longrightarrow \quad e=0 \eqno{\hbox{(2)}}$$for . A detecting matrix is said to be binary, bipolar, or ternary if and only if all of its entries belong to the set , or , respectively. Clearly, if a detecting matrix is binary or bipolar, it is also ternary. For example, $$A=\left[\matrix{1 & 0 & 1 & 1 \cr 1 & 1 & 0 & 0 \cr 0 & 1 & 1 & 0} \right] \quad {\hbox {and}} \quad D=\left[\matrix{1 & -1 & 1 \cr 1 & 1 & 0} \right]$$are binary and ternary detecting matrices, respectively.