有限链环R=F_p[u]/上长为p^sn对偶码结构  

Structure of dual codes over finite chain ring R=F_p[u]/with length of p^sn

作　　者：韩牟[1] 田立新[2] 赵加[1] 

机构地区：[1]江苏大学计算机科学与通信工程学院,江苏镇江212013 [2]江苏大学理学院,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2013年第6期736-740,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(61300229);中国博士后基金资助项目(2013M531283);江苏省博士后基金资助项目(1201037C);江苏大学高级专业人才科研启动基金资助项目(12JDG048)

摘　　要：为促进有限链环上循环码的编、译码在工程上的应用,研究了有限链环R=F p[u]/<uk>上长为psn重根循环码的对偶码的结构,利用有限链环R中的MS多项式,给出了扩环中的埃尔米特内积与环R中离散傅里叶变换系数之间的关系,并证明了码C的对偶码为C的零化子在共轭映射下的像,最终获得了环R上长为psn对偶码的结构.从而为有限链环R=F p[u]/<uk>上的编码和译码应用研究提供了理论依据,同时也为利用纠错码构造在实际应用中可行的具有抗量子特性的轻密码算法奠定了基础.In order to promote the application in project of dual codes over the finite chain ring,the structure of dual codes （N =p^sn） over R =Fp[u]/〈 u^k 〉 was investigated.By MS polynomial of cyclic codes in finite chain ring of R,the theorem of the relationship between Hermitian inner product in R and the coefficients of discrete Fourier transforms was derived.It was proved that dual codes of C were annihilator code C under the conjugate map image to obtain the structures of dual codes over R =Fp [u] / 〈 u^k 〉.A theoretical basis is provided for the application of coding and decoding codes over finite chain ring.The foundation is established for the feasible of the light-weight code-based cryptosystems with anti-quantum computing properties in practical application.

关 键 词：有限链环 重根循环码 对偶码 MS多项式 离散傅里叶变换 

分 类 号：TN911.22[电子电信—通信与信息系统]