Solution Manual For Coding Theory San Ling High Quality //top\\ Here

“Step 1: For length n=7 over GF(2), the cyclotomic cosets modulo 7 are: C0=0, C1=1,2,4, C3=3,5,6. Step 2: The minimal polynomials: m1(x) = x^3 + x + 1, m3(x) = x^3 + x^2 + 1. Step 3: If the code is cyclic, g(x) divides x^7-1 = (x-1)(x^3+x+1)(x^3+x^2+1). Step 4: For dimension 4, g(x) must be degree 3. Typically g(x) = m1(x) = 1 + x + x^3. Step 5: Verification: Multiply g(x) by (1+x+x^2+x^3) gives a codeword — check row ops. g(x) = 1 + x + x^3.”

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