两类支撑3-设计的线性码  

Two Classes of Linear Codes Supporting 3-design

作　　者：刘琪 唐春明[1] LIU Qi;TANG Chun-ming(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2023年第3期253-260,共8页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871058)。

摘　　要：代数编码与组合设计的交叉领域一直是近年来的研究热点。虽然长度为q+1的支撑3-设计的线性码的无穷类已经被构造出来了,但是目前已知的构造还非常稀少。综合利用代数编码理论、组合设计和群论,构造出了两类长度为q+1的支撑3-设计的线性码,并且确定了它们的参数。最后证明了这两类线性码的支集构成的集族在一般射影线性群PGL(2,q)的作用下是不变的。The cross field of algebraic coding and combinatorial design has been a research hotspot in recent years.The known structures of infinite classes of linear codes with length q+1 supporting 3-design are still very rare despite the construction of some infinite classes.Two classes of linear codes with length q+1 supporting 3-design are constructed and their parameters are determined by the algebraic coding theory,combinatorial design and group theory.Finally,it is proved that the set family composed of the supports of these two classes of linear codes is invariant under the action of general projective linear group PGL(2,q).

关 键 词：线性码 T-设计 维数 循环码 一般射影线性群 

分 类 号：O157.4[理学—数学] O29[理学—基础数学]