INTRODUCING TWO CLASSES OF OPTIMAL CODES DERIVED FROM ONE WEIGHT F qFq[u]-ADDITIVE CODES
Subject Areas : Algebraic Structures and Optimizationsadegh sadeghi 1 , narjes mohsenifar 2
1 - گروه ریاضی مرکز فارسان، واحد شهرکرد، دانشگاه آزاد اسلامی، شهرکرد، ایران
2 - Department of Electrical Engineering, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
Keywords: Additive code, constacyclic code, one weight code. ,
Abstract :
Let $\mathbb{F}_{q}$ be a finite field with $q$ elements where $q = p^{m}$, and $R=\mathbb{F}_{q}+u \mathbb{F}_{q}$ denotes the ring $\frac{\mathbb{F}_{q}[u] }{\langle u^{2}\rangle}$. For positive integers $\alpha$ and $\beta$, a nonempty subset $C$ of $\mathbb{F}_{q}^{\alpha}\times R^{\beta}$ is called an $\mathbb{F}_{q}\mathbb{F}_{q}[u]$-additive code if $C$ is an $R$-submodule of $\mathbb{F}_{q}^{\alpha}\times R^{\beta}$. In this paper, we study these codes with respect to homogenous and Lee weights. Among main results, by the Gray image of these codes, we obtain $[q^{2}+q, 2, q^{2}]$ and $[2(q+1), 2, 2q]$ one weight optimal codes over $\mathbb{F}_{q}$.
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