| TR#: | CS0336 |
| Class: | CS |
| Title: | On Generator Matrices Of MDS Codes |
| Authors: | R.M. Roth and G. Seroussi |
| CS0336.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. |
| Copyright | The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information |
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