Allerton 2015 Paper Abstract

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Dau, Son Hoang (University of Illinois at Urbana Champaign), Song, Wentu (Singapore University of Technology and Design), Sprintson, Alex (Texas A&M University), Yuen, Chau (Singapore University of Technology and Design)

Constructions of MDS Codes Via Random Vandermonde and Cauchy Matrices Over Small Fields

Scheduled for presentation during the Invited Session "Distributed Storage II" (ThB1), Thursday, October 1, 2015, 11:10−11:30, Library

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Coding Theory, Data Storage, Coding Techniques and Applications

Abstract

Vandermonde and Cauchy matrices are commonly used in the constructions of maximum distance separable (MDS) codes. However, when additional design constraints are imposed on the code construction in addition to the MDS requirement, a Vandermonde or Cauchy matrix may not always suffice. We discuss some related coding problems of that nature that arise in different practical settings. We present a useful technique to tackle the constrained coding problems that includes random selection of the evaluation points of a Vandermonde or a Cauchy matrix. Our solutions require small finite fields whose sizes are polynomial in the dimensions of the generator matrices. We believe that this technique will be useful for solving a broad range of coding problems.

 

 

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