New Sets of Binary and Ternary Sequences with Low Correlation

Matrix construction using cyclic shifts of a column

“…A disadvantage is low cryptographic security, owing to low linear complexity of the shift sequence. Quadratic shift sequence matrices can be punctured, columns inserted columns shortened or lengthened, with predictable results [4].…”

“…The twelve columns are described by a shift sequence modulo 10. This shift sequence can be converted into a perfect shift sequence modulo 5, [4] : 3,2,2,4,0,3,-,3,0,4,2,2. This produces a perfect matrix, by using it to shift (cyclically) a ternary Legendre sequence of length 5: 0,1,-1,-1,1.…”

“…where T r n m is the trace function, which takes the sum of conjugates (as defined in [11]). This shift sequence can be converted into a perfect shift sequence for two-dimensional matrices by the addition of an appropriate linear function [4]. Then, all differences appear equally frequently for all cyclic shifts of the shift sequence.…”