Binary Permutation Sequences as Subsets of Levenshtein Codes and Higher Order Spectral Nulls Codes

We obtain long binary sequences by concatenating the columns of (0,1)-matrices derived from permutation sequences. We then prove that these binary sequences are subsets of the Levenshtein codes, capable of correcting insertion/deletion errors and subsets of the higher order spectral nulls codes, with spectral nulls at certain frequencies