Technical Report CS0336

Title: On Generator Matrices Of MDS Codes
Authors: R.M. Roth and G. Seroussi
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.
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