Periodic complementary sets of binary sequences

Let PCSN p denote a set of p binary sequences of length N such that the sum of their periodic auto-correlation functions is a δ-function. In the 1990, B¨omer and Antweiler addressed the problem of constructing PCSN p . They presented a table covering the range p ≤ 12, N ≤ 50 and showing in which cases it was known at that time whether PCSN p exist, do not exist, or the question of existence is undecided. The number of undecided cases was rather large. Subsequently the number of undecided cases was reduced to 26 by the author. In the present note, several cyclic difference families are constructed and used to obtain new sets of periodic binary sequences. Thereby the original problem of B¨omer and Antweiler is completely solved. Mathematics Subject Classification: 05B20, 05B30

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Dragomir Z. Djokovic
• Keywords: Binary Sequences, CORR 2007, Education, Periodic Auto-correlation Functions, Undecided Cases