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Pure Mathematics 2024
型为tr的5-半循环可分组设计
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Abstract:
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.
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