Technical Report CS0336

TR#:CS0336
Class:CS
Title: On Generator Matrices Of MDS Codes
Authors: R.M. Roth and G. Seroussi
PDFCS0336.pdf
Abstract: It is shown that the family of q-ary generalized Reed-Solomon codes is identical to the family of q-ary linear codes generated by matrices of the form [I|A], where I is the identity matrix, and A is a generalized Cauchy matrix. Using Cauchy matrices, a construction is shown of maximal triangular arrays over GF(q), which are constant along diagonals in a Hankel matrix fashion, and with the property that every square sub-array is nonsingular. This solves an open problem posed by Singelton in [2]. By taking rectangular sub-arrays of the described trinagles, it is possible to construct generator matrices [I|A] of MDS codes, where A is a Hankel matrix.
CopyrightThe above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information

Remark: Any link to this technical report should be to this page (http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/1984/CS/CS0336), rather than to the URL of the PDF files directly. The latter URLs may change without notice.

To the list of the CS technical reports of 1984
To the main CS technical reports page

Computer science department, Technion
admin