"coset decoding"? I tried googling on that and, except for a few references to this forum( perhaps to your posts!) I got references to communications and information theory. You might get more help by posting under the computer areas.
Whoops! I saw the OP earlier but overlooked the absence of citation. Kirti, coset decoding is a topic covered in many textbooks including Larry L. Dornhoff and Franz E. Hohn, Applied Modern Algebra, MacMillan, 1977. When I Googled I found what appears to be an expository paper at a suitable level from H. A. Verrill (Mathematics, LSU); try this this pdf. And re [thread=195378]this thread[/thread], kirti, I think you did post in the most suitable forum, since this is a topic in algebraic coding theory which does indeed come down to linear algebra!