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find the status of the following generators related to two isolated, single bit errors.

a.) x+1

b,) x^4+1

c) x^7+x^6+1

d) x^15+x^14+1

please explain this with examples in detail
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1 Answer

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a. This is a very poor choice for a generator. Any two errors next to each other cannot be detected.
b. This generator cannot detect two errors that are four positions apart.
c. This is a good choice for this purpose.
d. This polynomial cannot divide xt + 1 if t is less than 32,768. A codeword with two isolated errors up to 32,768 bits apart can be detected by this generator.
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