Results 1 to 2 of 2

Math Help - what is the advantage of galois field

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    2

    what is the advantage of galois field

    could any one please answer the question

    What is the advantage of galois field .
    how it is used in reed-solomon decoder and BCH decoder . please explain with example
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    A simple way to see the use of a Field is to observe that in the generic communication design setting, we want to encode a k-bit string into an n-bit( n > k naturally) string so that the added redundancy can be used to combat the effect of noise. Any set of n-tuple can be thought of as a code. However a linear code facilitates easy encoding design and simpler decoding structures(though they may not be optimal) and hence we learn them in algebraic coding theory. A linear code is a vector space and vector spaces are built over Fields. Since most of the assumed source alphabet is finite, we talk about vector-spaces over finite fields, which are also termed Galois Fields.

    It's not easy to explain the idea behind RS-encoding decoding or BCH decoding in a simple chat. Lots of results from finite fields are used to establish properties of BCH codes/RS codes and to facilitate their decoding.

    So can you be more specific? Which part of BCH decoding have you not understood?

    One of the, many ways to do BCH decoding, is to use the extended Euclidean Division Algorithm to find the error locator polynomial and error magnitude polynomial. Thus we find and correct errors.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ring, field, Galois-Field, Vector Space
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 15th 2012, 03:25 PM
  2. Inverse in Galois field
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 19th 2011, 11:42 PM
  3. splitting field and galois groups
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 13th 2010, 08:24 PM
  4. Doubt in Galois Field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 17th 2009, 08:37 PM
  5. how to do arithmetic operations in galois field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 1st 2008, 05:09 AM

Search Tags


/mathhelpforum @mathhelpforum