Reed-Solomon Assignment

The parameters of the code are the following:

The chosen prime $p = 151$, and this is also the block-length $n$. The message is a polynomial $m(x)$ over $\mathbb{F}_{151}$ of degree 49 or less (and hence has $k = 50$ coefficients).

The encoding of $m(x)$ is the list of evaluations over all points in $\mathbb{F}_{151}$.

The distance of this code is $n - k + 1 = 102$ and hence we should be able to correct $51$ errors.

Below is the encoding of $m(x)$, after some $50$ corruptions.

rscode = [134, 141, 103, 86, 126, 149, 124, 24, 49, 114, 106, 122, 70, 8, 139, 80, 22, 89, 81, 34, 134, 77, 63, 126, 127, 53, 124, 142, 115, 9, 111, 78, 48, 110, 145, 66, 12, 107, 81, 60, 134, 144, 134, 35, 22, 48, 131, 46, 111, 116, 23, 85, 71, 117, 113, 63, 134, 31, 52, 97, 33, 138, 37, 120, 105, 26, 80, 39, 96, 116, 107, 141, 48, 77, 5, 65, 4, 146, 71, 62, 15, 71, 121, 141, 119, 21, 9, 59, 8, 74, 36, 110, 85, 88, 142, 78, 48, 117, 35, 4, 15, 88, 134, 41, 12, 70, 150, 19, 7, 129, 67, 133, 54, 41, 45, 101, 139, 137, 34, 1, 143, 53, 84, 78, 107, 19, 31, 71, 28, 110, 0, 112, 25, 32, 13, 120, 6, 75, 42, 92, 93, 147, 41, 94, 131, 87, 29, 81, 90, 5, 17]

Here: rscode[0] = 134 is supposed to be $m(0)$,

rscode[1] = 141 is supposed to be $m(1)$,

...

rscode[150] = 17 is supposed to be $m(150)$.

Question: Find the polynomial $m(x)$.