On generator matrices of MDS codes (Corresp.)

Author

Roth, Ron M. ; Seroussi, Gadiel

Volume

Issue

fYear

1985

fDate

11/1/1985 12:00:00 AM

Firstpage

826

Lastpage

830

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 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, where $A$ is a Hankel matrix. The parameters of the codes are $(n,k,d)$ , for $1 \\leq n \\leq q+ 1, 1 \\leq k \\leq n$ , and $d=n-k+1$ .

Keywords

Linear coding; Matrices; Reed-Solomon coding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1985.1057113

Filename

1057113

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=940935