N=1 super-Chern-Simons coupled to parity-preserving matter from Atiyah-Ward space-time

In this letter, we present the Parkes-Siegel formulation for the massive Abelian $N$$=$$1$ super-{\QED} coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from ($2$$+$$2$) to ($1$$+$$2$) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the ${\tau}_{3}$QED$_{1+2}$ coupled to a Chern-Simons term naturally comes out.