A generalization of modified de Bruijn sequences

In this paper, the sequences created by removing a single one from the longest run of ones in period 2n de Bruijn sequences (called de Bruijn-1 sequences) are the generalization of modified de Bruijn sequences (called de Bruijn-0 sequences). De Bruijn-0 sequences and de Bruijn-1 sequences are referred to as de Bruijn-0/1 sequences. The feedback functions and linear complexities are discussed. A new symmetry called TRUE/FALSE symmetry is proposed for de Bruijn-0/1 sequences. Detailed data of complexities is presented for orders 5 ≤ n ≤ 6.