代数几何码的Galois对偶码的Weil微分表示  

A representation of Galois dual codes of algebraic geometry codes via Weil differentials

作　　者：李家齐 马立明 Jiaqi Li;Liming Ma(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China;Wu Wen-Tsun Key Laboratory of Mathematics,School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学数学科学学院,安徽合肥230026 [2]中国科学技术大学数学科学学院吴文俊数学重点实验室,安徽合肥230026

出　　处：《中国科学技术大学学报》2023年第12期53-58,I0008,I0010,共8页JUSTC

基　　金：supported by the National Key Research and Development Program of China(2022YFA1004900);the USTC Research Funds of the Double First-Class Initiative(YD0010002004);the Fundamental Research Funds for the Central Universities(WK3470000020,WK0010000068).

摘　　要：Galois对偶码是Euclid对偶码和Hermite对偶码的推广。我们证明了函数域F=F_(p)^(e)上代数几何码C_(L,F)(D,G)的h-Galois对偶码是F′=F_(p)^(e)上的代数几何码C_(Ω,F′)(ϕ_(h)(D),ϕ_(h)(G)),其中,F′=F_(p)^(e)是一个与F=F_(p)^(e)有关的函数域,ϕ_(h)是从F到F′的同构映射,并且对任意a∈F_(p)^(e)满足ϕ_(h)(a)=a^(p)^(e-h).作为上述结果的应用,我们构造了一类h-Galois LCD MDS码。Galois dual codes are a generalization of Euclidean dual codes and Hermitian dual codes.We show that the-Galois dual code of an algebraic geometry code C_(L,F)(D,G)from function field F=F_(p)^(e)can be represented as an algebraic geometry code C_(Ω,F′)(ϕ_(h)(D),ϕ_(h)(G))from an associated function field F′=F_(p)^(e)with an isomorphismϕ_(h):F→F′satisfyingϕ_(h)(a)=a^(p)^(e-h)for all a∈F_(p)^(e).As an application of this result,we construct a family of h-Galois linear complementary dual maximum distance separable codes(h-Galois LCD MDS codes).

关 键 词：代数几何码 Galois对偶码 Galois线性补对偶码 MDS码 

分 类 号：O236.2[理学—运筹学与控制论]