New constructions of $2$-to-$1$ mappings over $\gf_{2^n}$ and their applications to binary linear codes

Yaqin Li, Kangquan Li, Qiancheng Zhang

The $2$-to-$1$ mapping over finite fields has a wide range of applications, including combinatorial mathematics and coding theory. Thus, constructions of $2$-to-$1$ mappings have a…