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check out the following functions in your Matlab help:
convmtx: Convolution matrix of Galois field vector
cosets: Produce cyclotomic cosets for Galois field
dftmtx: Discrete Fourier transform matrix in Galois field
filter (gf): 1-D digital filter over Galois field
gf: Create Galois field array
gftable: Generate file to accelerate Galois field computations
isprimitive: True for primitive polynomial for Galois field
log: Logarithm in Galois field
minpo: l Find minimal polynomial of Galois field element
mldivide: Matrix left division \ of Galois arrays
primpoly: Find primitive polynomials for Galois field
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