Problem with coding error in a cyclic code

[yagmai]

Hello guys,

how to solve this question?

For a cylic code, if an error pattern e(x) is detectable. show that its i cyclic shift e^(i) (x) is also detectable.

I was thinking this...

s(x) = r(x) mod g(x)

then look up the syndrome table, to find the error pattern.
What puzzled me is,

If let say I have a i cyclic shift r'(x), how do I know which s'(x) and what e'(x) I have. How do I actually show that i cyclic shift e^(i) (x) is also detectable. ?

Thanks a lot

 

[yagmai]

Re: Error Coding

Up, Any friend can help me with this question? Thanks