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MathGroup Archive 2005

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Re: Complete solution to a modular System of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60471] Re: Complete solution to a modular System of equations
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 17 Sep 2005 02:31:51 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, U.K.
  • References: <dgdvp1$1r5$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

mumat wrote:
> 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
> 
  	
Igor Gachkov's package _Error-correcting codes with Mathematica_ may be 
of interest. Check

http://library.wolfram.com/infocenter/MathSource/5085/

Hope this helps,
/J.M.


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