MATLAB Implementation of M-Sequence Generation Program with Automatic Primitive Polynomial Generator

In mathematics and communication fields, M-sequences are binary sequences with cyclic properties commonly used in digital signal processing and coding. To generate M-sequences, MATLAB programs can be implemented using linear feedback shift register (LFSR) structures. These programs typically employ primitive polynomials as feedback connections, where the polynomial coefficients determine the tap positions in the shift register. The automatic primitive polynomial generation algorithm involves checking irreducibility and primitivity conditions using MATLAB's polynomial factorization functions. For M-sequence generation, key functions include bitwise XOR operations for feedback computation and circular shifting techniques to maintain sequence periodicity. These programs enhance the efficiency and accuracy of digital signal processing and coding applications, making them widely adopted in practical implementations. The MATLAB code typically handles polynomial selection, register initialization, and sequence validation through built-in communications toolbox functions or custom algorithmic implementations.