MATLAB Code Implementation for M-Sequence Generation

An m-sequence is a type of pseudorandom number sequence commonly used in encryption, decryption, and various communication applications. To generate m-sequences in MATLAB, two key parameters must be defined: the primitive polynomial and the initial register values. The primitive polynomial determines the fundamental characteristics of the sequence, while the register initialization data controls the sequence length and periodicity.

Implementation typically involves configuring a Linear Feedback Shift Register (LFSR) where the primitive polynomial defines the feedback taps. Different initial register values produce m-sequences with varying lengths and periods through XOR operations and bit shifting. The MATLAB code would initialize the shift register with seed values, then iterate through clock cycles while applying polynomial-based feedback logic.

Beyond cryptographic applications, m-sequences are widely employed in communication systems (for spreading codes), radar signal processing, and satellite navigation (GPS gold codes). The MATLAB implementation can include functions for sequence validation, autocorrelation analysis, and period verification to ensure proper m-sequence properties.

Key MATLAB functions that may be utilized include bitwise operations (bitand, bitor), shift register emulation using arrays, and polynomial representation using coefficient vectors. The implementation should verify that the chosen polynomial is primitive using number theory checks to guarantee maximum sequence length.