Re: Complete solution to a modular System of equations ( Correction)

• To: mathgroup at smc.vnet.net
• Subject: [mg60513] Re: Complete solution to a modular System of equations ( Correction)
• From: "mumat" <csarami at gmail.com>
• Date: Mon, 19 Sep 2005 04:45:33 -0400 (EDT)
• References: <200509160750.DAA00817@smc.vnet.net><dgh4fn\$ng4\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Sorry Guess the 2^100 solutions ( binary vectors of length 200) using
MAGMA

http://magma.maths.usyd.edu.au/magma/htmlhelp/text598.htm

This is not very clear so let me point out a few things.

(1) You are not going to list 2^100 elements of anything.

>The Magma! listed all 2^100!!! i had tried that for the binary finite field F_2= Z_2=GF(2).

(2) You mention 2^(n-k) solutions. Is k meant to be the matrix rank?

>Yes, k is the rank of matrix in Z_2.

(3) You mention Z_p^n. This is the ring of integers modulo p^n. Did you
instead have in mind the Galois field of p^n elements? I assume not.
Did
you mean (Z_p)^n, the vector space of dimension n with elements in Z_p?

>Yes, I meant the vector space (Z_p)^n. Sorry, I had to parenthesize Z_p!

Assuming that last is what you have in mind, just find a null space
basis with NullSpace, then take all possible combinations.

> As you see i have computed all possible combinations... but's it's too slow.