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>