What is the total length for the sequence for a linear feedback shift register generated with a maximum length sequence, before repeating?
The duration of the linear feedback shift register (LFSR) in number of "chips" is $2^N-1$ where N is the number of states in the shift register (and order of the generator polynomial), and chips refers to each unique output that is generated in the sequence. This is assuming that you are using a maximum length sequence in the implementation of your shift register, which means the generator polynomial is both primitive and irreducible in GF(2).
Primitive: Repeated multiplying by x (representing a shift of one position in the shift register) will generate every possible state (except for the all 0 state). If the generator is not primitive, possible states (combinations of the register values) will be skipped and the sequence will be less than $2^N-1$ in length before repeating.
Irreducible: Cannot be factored, see example:
Reducible: $1+x+x^2+x^3 = (1+x^2)(1+x)$
Note the above polynomials are in GF(2) so the only elements are 0,1. 1+1=0, 0-1=1, etc
All primitive polynomials are irreducible but the converse is not true!
Primitive and irreducible polynomials are well tabulated. For a handy table of primitive and irreducible polynomials in GF(2), see Peterson's Table of Irreducible Polynomials
The graphic below shows the two common implementation approaches for the LFSR from the generator polynomial, in this case N=4, using generator polynomial $1+x^3+x^4$ which would generate $2^4-1=15$ chips before repeating: