Instances of the $ \mathfrak{G}$-construction

The $ \mathfrak{G}$-construction algorithm is technically complicated and will be relegated to Section 4. A generating mapping uniquely determines a corresponding family of codes, known as a $ \mathfrak{G}$-family, produced by the $ \mathfrak{G}$-construction. In this section we shall analyze various generating mappings that can be used to design these families for specific decoding needs.