Overview

The following gives the primitive polynomials with the least number of terms which may be used to generate an autonomous maximum length pseudorandom sequence (an M-sequence) from an n-stage linear feedback shift register (LFSR). Alternatives are possible in many cases, particularly as n increases.

Recall from Chapter 3 that the primitive polynomial has the form:

where a _i ? {0, 1}. The polynomial:

represents a generating polynomial for n = 12. For convenience in the following table we will merely record the powers of x in reverse order from the above, for example:

This indicates a 12-stage LFSR with taps at n = 12, 7, 4 and 3 exclusive-ORed back to the serial input of the LFSR. The length of the shift register n will therefore always be the first (left-hand) number in this table.

Additional comments are given following the table.