Hi There, I am a bit confused. If I recall correctly, I have read/learned that any submatrix of a generator matrix is invertible. If one considers the non-systematic Reed-Solomon code generated by a Vandermonde matrix, this is true. However, if one considers the "Reed-Solomon" code generated by [I | C], where I is a k X k identity matrix, and C is a (k X n-k) Cauchy matrix, not every submatrix is invertible. However, every k X k submatrix will be invertible. Could someone clarify? Also, the second code that I discussed, is that a Reed-Solomon code? In literature I see that some people regard it as a Reed-Solomon code. The two definitions that I know of for Reed-Solomon codes are either the Vandermonde generator matrix (Reed and Solomon's original work) or the n-k consecutive roots generator polynomial? Your time and effort will greatly be appreciated Jaco

# Regarding Generator Matrices of MDS codes?

Started by ●July 19, 2006

Reply by ●July 19, 20062006-07-19

<jaco.versfeld@gmail.com> wrote in message news:1153314649.845377.152090@m79g2000cwm.googlegroups.com...> If I recall correctly, I have read/learned that > any submatrix of a generator matrix is invertible.It is not true in general that any submatrix of a generator matrix is invertible. The statement is not true for Reed-Solomon (more generally, MDS) codes unless the assertion includes the further qualification that the submatrix is of size k x k. So, either your recollection is faulty or you read/learned something that is incorrect.> However, if one considers the "Reed-Solomon" code generated by [I | C], > where I is a k X k identity matrix, and C is a (k X n-k) Cauchy matrix, > not every submatrix is invertible. However, every k X k submatrix will > be invertible.>Could someone clarify?It is an axiom of the (much maligned in the U.S.) scientific method that a theory that does not fit the facts must be discarded or modified. You have a fact here that is counter to your theory that every submatrix of a generator matrix is invertible. What do you want to do with your theory?

Reply by ●July 24, 20062006-07-24