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Complete solution to a modular System of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg60450] Complete solution to a modular System of equations
• From: "mumat" <csarami at gmail.com>
• Date: Fri, 16 Sep 2005 03:50:52 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

In coding theory one is intersted to find the dual code of a given
code. To do this one has to solve a modular linear equation such as:



eq = {a + b + d == 0, a + c + d == 0, b + c + d == 0}

lhs = {{1, 1, 0, 1}, {1, 0, 1, 1}, {0, 1, 1, 1}}; rhs = {0, 0, 0};

LinearSolve[lhs,{0,0,0},Modulus->2]

Out[52]=
{0,0,0,0}

as you see it returns only one solution. How can I find all solutions.
The number of solutions is a power of 2. For about example there is
exacly one more solution which is

{1,1,1,0}.

Is there any function in Mathematica to do this? or I should start
writing my own code?

thanks for your help in advance!

regards,

chekad

• Follow-Ups:
  • Re: Complete solution to a modular System of equations
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Complete solution to a modular System of equations
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>