Error-correcting codes in attenuated space over finite fields

Several bounds on the size of (n+l,M,d,(m,0))q(n+l,M,d,(m,0))q codes in attenuated space over finite fields are provided in this paper. Then, we prove that codes in attenuated space attain the Wang–Xing–Safavi-Naini bound if and only if they are certain Steiner structures.