54. Let C be a binary (15,10) cyclic code generated by 8(x)= (x+1)(x++1) and C be...

 

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54. Let C₁ be a binary (15,10) cyclic code generated by 8₁(x)= (x+1)(x+²+1) and C₂ be another binary (15,10) cyclic code generated by h(x) = (x+1)(x+x+1). (1) Is (11011 00101 00000) € C₁ C₂? (ii) What is the generator polynomial for the code C = C₁ C₂? (iii) How many cyclic subspaces are contained in C₁? 54. Let C₁ be a binary (15,10) cyclic code generated by 8₁(x)= (x+1)(x+²+1) and C₂ be another binary (15,10) cyclic code generated by h(x) = (x+1)(x+x+1). (1) Is (11011 00101 00000) € C₁ C₂? (ii) What is the generator polynomial for the code C = C₁ C₂? (iii) How many cyclic subspaces are contained in C₁?

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i To determine if the codeword 110110010100000 is in C12 we need to check if it satisfies the parity... View the full answer