On generator matrices of MDS codes (Corresp.)
- 1 November 1985
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 31 (6) , 826-830
- https://doi.org/10.1109/tit.1985.1057113
Abstract
It is shown that the family ofq-ary generalized Reed-Solomon codes is identical to the family ofq-ary linear codes generated by matrices of the form[I|A], whereIis the identity matrix, andAis 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 subarray is a nonsingular matrix. By taking rectangular subarrays of the described triangles, it is possible to construct generator matrices[I|A]of maximum distance separable codes, whereAis a Hankel matrix. The parameters of the codes are(n,k,d), for1 \leq n \leq q+ 1, 1 \leq k \leq n, andd=n-k+1.Keywords
This publication has 1 reference indexed in Scilit:
- Maximum distanceq-nary codesIEEE Transactions on Information Theory, 1964