Unit Zq-simplex codes of type and zero divisor Zq-simplex codes

In this paper, we have punctured unit $mathbb{Z}_q$-Simplex code  and constructed a new code called unit $mathbb{Z}_q$-Simplex code of type $alpha$. In particular, we find the parameters of  these codes and have proved that it is an $left[phi(q)+2, ~hspace{2pt} 2, ~hspace{2pt} phi(q)+2 - frac{phi(q)}{phi(p)}right]$ $mathbb{Z}_q$-linear code $text{if} ~ k=2$ and $left[frac{phi(q)^k-1}{phi(q)-1}+phi(q)^{k-2}, ~k,~ frac{phi(q)^k-1} {phi(q)-1}+phi(q)^{k-2}-left(frac{phi(q)}{phi(p)}right)left(frac{phi(q)^{k-1}-1}{phi(q)-1}+phi(q)^{k- 3}right)right]$ $mathbb{Z}_q$-linear code if $k geq 3, $ where $p$ is the smallest prime divisor of $q.$  For $q$ is a prime power and rank $k=3,$ we have given the  weight distribution of  unit $mathbb{Z}_q$-Simplex codes  of type $alpha$. Also, we have introduced some new code from  $mathbb{Z}_q$-Simplex code called zero divisor $mathbb{Z}_q$-Simplex code and proved that it is an $left[ frac{rho^k-1}{rho-1}, hspace{2pt} k, hspace{2pt} frac{rho^k-1}{rho-1}-left(frac{rho^{(k-1)}-1}{rho-1}right)left(frac{q}{p}right) right]$ $mathbb{Z}_{q}$-linear code, where $rho = q-phi(q)$ and $p$ is the smallest prime divisor of $q.$ Further, we obtain  weight distribution of  zero divisor $mathbb{Z}_q$-Simplex code for rank $k=3$ and $q$ is a prime power.