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. thanks much for your comments, Daniel.

**Follow-Ups**:**Re: Re: Complete solution to a modular System of equations ( Correction)***From:*Daniel Lichtblau <danl@wolfram.com>

**References**:**Complete solution to a modular System of equations***From:*"mumat" <csarami@gmail.com>