# How to understand the syndrome of Reed Solomon code

Started by September 20, 2010
```Hi,

In the following description of RS code, Syndrome S first said the
remaider of R mod G. Then, it is said C is multiple of G. I feel that
it is controversy here. C mod G has 0 remainder? Could you explain it
to me? thanks a lot

....................
Let C be the code word without any errors, R be the received code word
and E be any error that
the channel introduces. The encoder takes the data D to be encoded and
encodes it as a
codeword C, which is a multiple of the generator polynomial G for the
case of systematic codes
by adding 2T parity words after the K data bytes. The syndrome S can
then be defined as S = R
mod G and is the remainder obtained by dividing the received code word
by the generator
polynomial G. The received code word R can then be expressed as R = C
+ E where E is the
associated channel error. Since C is a multiple of G by definition, S
actually evaluates to the
following:
S = E mod G.
```