Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

One weight SR-additive codes

Document Type : Original Paper

Authors
Saadoun Mahmoudi Nabikandi 1
Ali Eisapour ‎Khasadan 2
shahram mehry 1
1 ‎Department of Mathematics‎, ‎Faculty of Mathematical Sciences and Statistics‎, ‎Malayer University‎, ‎Malayer‎, ‎Iran
2 Department of Mathematics‎, ‎Faculty of Mathematical Sciences and Statistics‎, ‎Malayer University‎, ‎Malayer
10.22055/jamm.2025.44671.2196
Abstract
‎Let ‎‎$‎q$ be a power of a prime ‎number,‎ ‎$ S = ‎‎\mathbb{‎F}‎‎_{q}[u]‎/ ‎\langle u^{2} ‎\rangle$‎‎‎‎ ‎and‎ $ R=‎‎‎‎‎ ‎‎\mathbb{‎F}‎_{q}[u]‎/ ‎\langle u^{3} ‎\rangle ‎$‎. ‎For ‎positive ‎integers ‎‎$‎‎\alpha‎$ and ‎$‎\beta‎‎‎$‎, a‎ ‎nonempty ‎subset ‎‎$‎C$ of ‎ ‎$ S^{\alpha}\times R^{\beta}$ ‎is ‎called ‎an ‎‎$‎SR$-additive code if ‎$‎C$ is an ‎$‎R$-submodule of ‎$S^{\alpha}\times R^{‎\beta}‎‎$. In this paper, we study one weight ‎$‎SR$-additive codes. More ‎precisely, ‎we ‎define a‎ ‎weight ‎function ‎on ‎this ‎class ‎of ‎codes.‎ The relations between the length, size and weight of the code are ‎presented. ‎At ‎the ‎end, ‎we ‎define a ‎Gra‎y ‎map ‎over ‎these ‎codes. ‎By ‎using ‎the ‎define‎d‎ ‎G‎ray ‎map, a‎ ‎subclass ‎of ‎optimal ‎codes ‎over ‎‎$\mathbb{‎F}‎‎_{q}$ ‎is ‎constructed‎.
Keywords
‎One weight additive codes‎‎
SR-additive codes‎
‎Gray maps‎
Chain ring
Subjects
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  • Receive Date 01 September 2023
  • Revise Date 21 April 2025
  • Accept Date 10 June 2025