2020年,Wu等(IEEE Transactions on Information Theory,2020,66(6):3657-3663.)运用简单复合体,在环F_(2)+u F_(2)(u^(2)=0)上构造了2类少重量二元码.基于此工作,利用简单复合体,在有限域F_(2)上构造2类新的最优少重量二元码,并利用初...2020年,Wu等(IEEE Transactions on Information Theory,2020,66(6):3657-3663.)运用简单复合体,在环F_(2)+u F_(2)(u^(2)=0)上构造了2类少重量二元码.基于此工作,利用简单复合体,在有限域F_(2)上构造2类新的最优少重量二元码,并利用初等的方法和技巧,得到这2类码的重量分布,并证明它们的参数都满足Griesmer界;最后给出2个具体例子.展开更多
Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub&g...Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.展开更多
文摘2020年,Wu等(IEEE Transactions on Information Theory,2020,66(6):3657-3663.)运用简单复合体,在环F_(2)+u F_(2)(u^(2)=0)上构造了2类少重量二元码.基于此工作,利用简单复合体,在有限域F_(2)上构造2类新的最优少重量二元码,并利用初等的方法和技巧,得到这2类码的重量分布,并证明它们的参数都满足Griesmer界;最后给出2个具体例子.
文摘Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.
