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

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Prabu J.; Mahalakshmi J.; Santhakumar S.

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Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2023 | Volume:8 | Issue:2 Page(s): 327-348

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Title

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

Author(s)

Prabu J. | Mahalakshmi J. | Santhakumar S. | Issue Writer Certificate

Keywords

Unit Zq-Simplex codes of type α

Unit Zq-MacDonald code

Zero divisor Zq-Simplex code and Weight distribution

Abstract

In this paper, we have punctured unit Zq-Simplex code and constructed a new code called unit Zq-Simplex code of type _. 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-1/ Φ, (q)-1 + Φ, (q)k-2, k, Φ, (q)k-1/ Φ, (q)-1 + Φ, (q)k-2 –,(Φ, (q) / Φ, (p)) (Φ, (q)k-1 –,1/ Φ, (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 [ρ, k-1/ ρ,-1, k, ρ, k-1/ ρ,-1 –,(ρ, (k-1) –,1/ ρ,-1) (q/p)] 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.

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APA: Copy

Prabu, J., Mahalakshmi, J., & Santhakumar, S.. (2023). Unit Zq-simplex codes of type α,and zero divisor Zq-simplex codes. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 8(2), 327-348. SID. https://sid.ir/paper/1057796/en

Vancouver: Copy

Prabu J., Mahalakshmi J., Santhakumar S.. Unit Zq-simplex codes of type α,and zero divisor Zq-simplex codes. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION[Internet]. 2023;8(2):327-348. Available from: https://sid.ir/paper/1057796/en

IEEE: Copy

J. Prabu, J. Mahalakshmi, and S. Santhakumar, “Unit Zq-simplex codes of type α,and zero divisor Zq-simplex codes,” COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, vol. 8, no. 2, pp. 327–348, 2023, [Online]. Available: https://sid.ir/paper/1057796/en

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