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?
>
>
> regards,
>
>

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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