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Questions tagged [galois-field]

Galois field also knows as finite field in abstract algebra is a field that contains a finite number of elements.

A Galois field, also knows as finite field in abstract algebra, is a field that contains a finite number of elements.

A field is an algebraic structure with multiplication and addition, where every element has a multiplicative inverse, and all elements commute with each other.

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Speed up gf(eye(x)) a.k.a. Speed up Galois field creation for sparse matrices

From the documentation (communications toolbox) x_gf = gf(x,m) creates a Galois field array from the matrix x. The Galois field has 2^m elements, where m is an integer between 1 and 16. Fine. The effort for big matrices grows with the number of…
Tommy
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What is wrong in this Discrete Integration with Galois Fields in Matlab

I want to implement Discrete Integration with Galois Fields in Matlab where the time step is not constant. Assume that it is this: My attempt function [ int ] = integrate_matlab( YDataVector, a, b ) %integrate_matlab Calculate the discrete…
Léo Léopold Hertz 준영
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How does gfdiv differ from "\" for Galois field in Matlab?

I two variables YDataVector and diff which are (255 x 1 gf) that is Galois vectors. I need to do division between the two variables like for real numbers YDataVector = ( YDataVector - 1 ) / diff; I found that there is also the command gfdiv, which…
Léo Léopold Hertz 준영
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How to visualise Galois Vector Array in Matlab

I have this data, (255x1 gf). It is FFT processed signal data. I want to visualise it. I do not find any conversion function back to integer or double, or any plotting function for Galois Vector Array. I found that you can run fftshift to the data…
Léo Léopold Hertz 준영
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Regarding creation of Galois field

When I do this: >> data_source = randsrc(1,493, 0:1); >> msg=gf(data_source,9); %creation of Galois field in Workspace it creates a variable as: msg=<1x493 gf>. and when I open it in variable-editor, it is showing gf object: 1-by-65 as first entry…
user2888999
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How do I compute logarithms in cryptography?

I am trying to perform non-linear functions on bytes to implement SAFER+. The algorithm requires computing base-45 logarithm on bytes, and I don't understand how to do it. log45(201) = 1.39316393 When I assign this to a byte, the value is truncated…
Eng. Aws
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Galois Reed Solomon

I work on a project about cryptosystem using Reed Solomon codes and it is using implementation of Galois package on Python. As I know, Reed Solomon codes based and work on polynomial representation but using the galois package, it can build the…
heidii
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In python, how to find a primitive element of finite field?

Say, I want a finite field containing $2^n$ elements for some positive $n$. How to get a single random primitive element in Python, different from that provided by the Conway polynomial? I know that Python's Galois library gives the option to…
Julian Osorio
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Generate all binary strings/patterns of a given length which are unique even when rotated

I need an algorithm that behaves like this: In: 1 Out: 0, 1 In: 2 Out: 00, 01/10, 11 In: 3 Out: 000, 001/010/100, 011/110/101, 111 In: 4 Out: 0000, 0001/0010/0100/1000, 0011/0110/1100/1001, 0101/1010, 0111/1110/1101/1011, 1111 of the separated using…
Sean Goff
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Is there a way to Forward Error Correct (FEC RS) an Alphabet of 36 chars?

Case: We want to Encode an 8 Character code to 10 Character code with adding 2 Forward Error Correcting Reed-Solomon Characters(so suffix 2 Error Correcting Chars). Example Code I'm using this Library C# FEC Reed-Solomon Library. I'm having a…
RennieM
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The function np.dot multiplies the GF4 field matrices for a very long time

Multiplies large matrices for a very long time. How can this problem be solved. I use the galois library, and numpy, I think it should still work stably. I tried to implement my GF4 arithmetic and multiplied matrices using numpy, but it takes even…
Дима Бобрикович
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Power of 3 of a Binary Number in GF(2^6) in VHDL?

I tried myself in a GF(2^4). With the minimal polynom z^4+z+1: a(z) = a0 + a1.z + a2.z^2 + a3.z^3 [a(z)]^3 = a0 + a1.z^3 + a2.z^6 + a3.z^9 = a0 + a1.z^3 + a2.(z^3 + z^2) + a3.(z^3+z) = a0 + a1.z + a2.z^2 + (a1+a2+a3).z^3 Now i have to replace (a0,…
Sir Kadse
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How to perform reduced row echelon form on a non-square GF matrix (GF(2^8)) in matlab

%GF(2^8) m=8 mat1 = gf([160 28 233 185 176],8); result1 = gf([160 28 233 185 176],8)/gf([160],8) % 1 77 174 32 220 [R,jb] = rref([1 77 174 32 220;189 244 80 245 190]) I use the result from result1 as 1st row…
Beneyaz Ara Begum
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modulo reduction in field of non primitive order

I'm getting started with AES and need to calculate the inverse for S-byte table. I'm trying to generate exponential and logarithm table for inversion with generator 3. The exponents works fine till I reach 3 ^ 8 which is 0xff. Exponential table …
Shanks Limbu
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Error correcting codes for short (7-10 bits) windowed reads from cyclic tapes

I have an array of N bits written on a cyclic tape. I read a sequence of M symbols starting from a random place on the tape. I was thinking about Reed Solomon error correction trying all possible starting points of the message, but all RS…
Moonwalker
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