$7\mathrm{.}30$ A binary $15,5-$cyclic code is generated by $g(x)=1+x+x^2+x^4+x^5+x^8+x^{10}.$ Construct a parity$-$check matrix of the form $(A|).$ Decode the following words using error trapping:

$($a$)011111110101000$ ;

$($b$)100101111011100.$