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RISS 인기검색어
- 검색키워드
- 저자 : Saadoun Mahmoudi (검색결과 2 건)
- 무료
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- 유료
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Saadoun Mahmoudi,Karim Samei 대한수학회 2019 대한수학회보 Vol.56 No.5
In this paper, we introduce $SR$-additive codes as a generalization of the classes of $\mathbb{Z}_{p^r}\mathbb{Z}_{p^s}$ and $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes, where $S$ is an $R$-algebra and an $SR$-additive code is an $R$-submodule of $S^{\alpha}\times R^{\beta}$. In particular, the definitions of bilinear forms, weight functions and Gray maps on the classes of $\mathbb{Z}_{p^r}\mathbb{Z}_{p^s}$ and $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes are generalized to $SR$-additive codes. Also the singleton bound for $SR$-additive codes and some results on one weight $SR$-additive codes are given. Among other important results, we obtain the structure of $SR$-additive cyclic codes. As some results of the theory, the structure of cyclic $\mathbb{Z}_{2}\mathbb{Z}_{4}$, $\mathbb{Z}_{p^r}\mathbb{Z}_{p^s}$, $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$, $(\mathbb{Z}_{2})(\mathbb{Z}_{2} + u\mathbb{Z}_{2} + u^{2}\mathbb{Z}_{2})$, $(\mathbb{Z}_{2} + u\mathbb{Z}_{2} )(\mathbb{Z}_{2} + u\mathbb{Z}_{2} + u^{2}\mathbb{Z}_{2})$, $(\mathbb{Z}_{2})(\mathbb{Z}_{2} + u\mathbb{Z}_{2} + v\mathbb{Z}_{2})$ and $(\mathbb{Z}_{2} + u\mathbb{Z}_{2} )(\mathbb{Z}_{2} + u\mathbb{Z}_{2} + v\mathbb{Z}_{2})$-additive codes are presented.
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Mahmoudi, Saadoun,Samei, Karim Korean Mathematical Society 2019 대한수학회보 Vol.56 No.5
In this paper, we introduce SR-additive codes as a generalization of the classes of ${\mathbb{Z}}_{p^r}{\mathbb{Z}}_{p^s}$ and ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-additive codes, where S is an R-algebra and an SR-additive code is an R-submodule of $S^{\alpha}{\times}R^{\beta}$. In particular, the definitions of bilinear forms, weight functions and Gray maps on the classes of ${\mathbb{Z}}_{p^r}{\mathbb{Z}}_{p^s}$ and ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-additive codes are generalized to SR-additive codes. Also the singleton bound for SR-additive codes and some results on one weight SR-additive codes are given. Among other important results, we obtain the structure of SR-additive cyclic codes. As some results of the theory, the structure of cyclic ${\mathbb{Z}}_2{\mathbb{Z}}_4$, ${\mathbb{Z}}_{p^r}{\mathbb{Z}}_{p^s}$, ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$, $({\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+u^2{\mathbb{Z}}_2)$, $({\mathbb{Z}}_2+u{\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+u^2{\mathbb{Z}}_2)$, $({\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+v{\mathbb{Z}}_2)$ and $({\mathbb{Z}}_2+u{\mathbb{Z}}_2)({\mathbb{Z}}_2+u{\mathbb{Z}}_2+v{\mathbb{Z}}_2)$-additive codes are presented.
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