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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 42EQ

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In the Shamir secret sharing scheme, we distribute a secret among q different users as
follows. If our secret a message (m₁, ..., mk) from V(k, q) then, we encode it as a
codeword of the Reed-Solomon RS (9) and give one coordinate to each user. In this
problem, we will use q = 7, k = 4 and the parity check matrix H₁ below for RS4(7).
HA
=
1
1
01
1 1
1 1
2 3 4 5 6
4224 1
1. Write a generator matrix for RS4 (7) of the form Hq-k.

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