نوع مقاله : مقاله پژوهشی
عنوان مقاله English
نویسندگان English
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.
کلیدواژهها English
