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 > >