Publication

Abstract : In this paper, we have punctured unit Zq-Simplex code and constructed a new code called unit Zq-Simplex code of type α. In particular, we find the parameters of these codes and have proved that it is an [ϕ(q)+2, 2, ϕ(q)+2−ϕ(q)ϕ(p)] Zq-linear code if k=2 and [ϕ(q)k−1ϕ(q)−1+ϕ(q)k−2, k, ϕ(q)k−1ϕ(q)−1+ϕ(q)k−2−(ϕ(q)ϕ(p))(ϕ(q)k−1−1ϕ(q)−1+ϕ(q)k−3)] Zq-linear code if k≥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 Zq-Simplex codes of type α. Also, we have introduced some new code from Zq-Simplex code called zero divisor Zq-Simplex code and proved that it is an [ρk−1ρ−1,k,ρk−1ρ−1−(ρ(k−1)−1ρ−1)(qp)] Zq-linear code, where ρ=q−ϕ(q) and p is the smallest prime divisor of q. Further, we obtain weight distribution of zero divisor Zq-Simplex code for rank k=3 and q is a prime power.