On $q$-ary shortened-$1$-perfect-like codes

Minjia Shi, Rongsheng Wu, Denis S. Krotov

We study codes with parameters of $q$-ary shortened Hamming codes, i.e., $(n=(q^m-q)/(q-1),q^{n-m},3{)}_q$. Firstly, we prove the fact mentioned in 1998 by Brouwer et al. that such…