Editing Maximum length sequence (section)

===Polynomial interpretation===
A [[polynomial]] over [[Galois field|GF(2)]] can be associated with the linear-feedback shift register. It has degree of the length of the shift register, and has coefficients that are either 0 or 1, corresponding to the taps of the register that feed the [[xor]] gate. For example, the polynomial corresponding to Figure 1 is <math>x^4+x+1</math>.

A necessary and sufficient condition for the sequence generated by a LFSR to be maximal length is that its corresponding polynomial be [[Primitive polynomial (field theory)|primitive]].<ref>"Linear Feedback Shift Registers-Implementation, M-Sequence Properties, Feedback Tables"[http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm], New Wave Instruments (NW), Retrieved 2013.12.03.</ref>