| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
