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Reed-Solomon Codes

1. Which of the following code can be the dual code of (7,3,5)(7,3,5)?
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2. Which of the following field can construct (63,57,7)(63,57,7) RS code?
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The code generated by the matrix G=[110000101000100100100010100001]G = \begin{bmatrix} 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 \end{bmatrix} is
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4. The code generated by the matrix G=[111111123456142241116166124421] G = \begin{bmatrix} 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 & 5 & 6 \\ 1 & 4 & 2 & 2 & 4 & 1 \\ 1 & 1 & 6 & 1 & 6 & 6 \\ 1 & 2 & 4 & 4 & 2 & 1 \end{bmatrix} over the field F7\mathbb{F}_{7} is Reed-Solomon code
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5. Message polynomial of the bit stream 010110111100010110111100 over the Galois field F23[X]\mathbb{F}_{2^{3}}[X] is
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6. Consider (7,4,4)(7,4,4) RS code over Galois field F23={0,1,α,α2,α3=1+α,α4=α+α2,α5=1+α+α2,α6=1+α2}\mathbb{F}_{2^{3}} = \{ 0, 1, \alpha, \alpha^{2}, \alpha^{3} = 1+\alpha, \alpha^{4} = \alpha+\alpha^{2}, \alpha^{5}=1+\alpha+\alpha^{2}, \alpha^{6}= 1+\alpha^{2} \} with evaluation set {α1=1,α2=α,α3=α2,α4=α3,α5=α4,α6=α5,α7=α6} \{\alpha_{1} = 1, \alpha_{2} = \alpha, \alpha_{3} = \alpha^{2}, \alpha_{4} = \alpha^{3}, \alpha_{5} = \alpha^{4},\alpha_{6} = \alpha^{5}, \alpha_{7} = \alpha^{6} \}. Then the encoded message bit stream of 010110111100010110111100 (same as the above question) is
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