Maximum Length Sequences

The m-sequences are used in numerous applications in digital communication systems like spread-spectrum system.

Maximum length sequence (MLS) is a type of pseudorandom binary sequence which can be generated by maximal length shift registers (MLSR). These sequences may be represented as coefficients of irreducible polynomials. Except the near-zero DC term, m-sequences are spectrally flat. The period of of the generated sequence of an m-stage shift register, is at most $2^{m}-1$.

The sequence $a_{n}$ is generated by the shift registers and it can be formulated as $a_{n}= c_{1}a_{n-1}+c_{2}a_{n-2}+...+c_{r}a_{n-r}=\sum_{i=1}^{r} c_{i} a_{n-i}$ where $c_{r}$ is the connection weight.