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Su, Xiaowei; Wang, Lidong; Tian, Zihong
Discrete mathematics, November 2022, 2022-11-00, Letnik: 345, Številka: 11Journal Article
Motivated by the application in geometric orthogonal codes (GOCs), Wang et al. introduced the concept of generalized perfect difference families (PDFs), and established the equivalence between GOCs and a certain type of generalized PDFs recently. Based on the relationship, we discuss the existence problem of generalized (n×m,K,1)-PDFs in this paper. By using some auxiliary designs such as semi-perfect group divisible designs and several recursive constructions, we prove that a generalized (n×m,{3,4},1)-PDF exists if and only if nm≡1(mod6). The existence of a generalized (n×m,{3,4,5},1)-PDF is also completely solved possibly except for a few values. As a consequence, some variable-weight perfect (n×m,K,1)-GOCs are obtained.
