型为t^r的5-半循环可分组设计

Semi-Cyclic Group Divisible Design of Type t^r with Block Size 5

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tr,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。

Semi-cyclic group divisible design has many applications in combinatorial coding. The necessary condition of semi-cyclic group divisible design of type tr 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.