Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Complete solution to a modular System of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60466] Re: [mg60450] Complete solution to a modular System of equations
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sat, 17 Sep 2005 02:31:47 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

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
> 
> 


  • Prev by Date: calling a C executable from within Mathematica
  • Next by Date: Re: Complete solution to a modular System of equations
  • Previous by thread: Re: Complete solution to a modular System of equations
  • Next by thread: Re: Complete solution to a modular System of equations