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Re: Complete solution to a modular System of equations


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

soln=Reduce[eq,{a,b,c,d},Modulus->2]

a == C[1] && b == C[1] && c == C[1] && d == 0

List@@Last/@soln/.{{C[1]->0},{C[1]->1}}

{{0, 0, 0, 0}, {1, 1, 1, 0}}


Bob Hanlon

> 
> From: "mumat" <csarami at gmail.com>
To: mathgroup at smc.vnet.net
> Date: 2005/09/16 Fri AM 03:50:52 EDT
> Subject: [mg60466] [mg60450] Complete solution to a modular System of equations
> 
> 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
> 
> 


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