%0 Journal Article
%T 型为t<sup>r</sup>的5-半循环可分组设计<br>Semi-Cyclic Group Divisible Design of Type t<sup>r</sup> with Block Size 5
%A 杜珺
%A 黄月梅
%J Pure Mathematics
%P 335-340
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/PM.2024.141034
%X 半循环可分组设计在组合编码中有着广泛的应用。根据半循环可分组设计的定义，给出型为t<sup>r</sup>，区组长度为5的半循环可分组设计存在的必要条件。再利用循环差阵、t-正则的循环填充及两种递归构造法，得到了型为tr，区组长度为5的半循环可分组设计存在的若干充分条件。<br />
Semi-cyclic group divisible design has many applications in combinatorial coding. The necessary condition of semi-cyclic group divisible design of type t<sup>r</sup> with block size 5 was obtained from the definition. In addition, several spectrums of semi-cyclic group divisible design with block size 5 were obtained by employing cyclic difference matrix, t-regular cyclic packing with the aid of two recursive constructions.
%K 半循环可分组设计，循环差阵，循环填充，递归构造<br>Semi-Cyclic Group Divisible Design
%K Cyclic Difference Matrix
%K Cyclic Packing
%K Recursive 
Construction
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=80320