1
vote
1answer
37 views

Cyclic Codes over $GF(q)$

Does the set of cyclic codewords / codeword polynomials themselves form a field ? I think they donot because the modulo operation is with respect to $x^n-1$ which is not a prime polynomial. Also the ...
3
votes
0answers
172 views

Bachelor Thesis - Galois Theory Research Topics?

I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was ...
2
votes
2answers
126 views

Generator Polynomial and Minimum Distance

Given a generator polynomial, how do I calculate minimum distance for the code. I am working in GF(2). A particular case of interest is the cyclic code of length $9$ generated by $$ ...
1
vote
2answers
150 views

find the degree of a minimal polynomial for a galois field element in an efficient way (by hand)

I stumbled upon the following question in the problem section of a book on coding theory. A galois field $GF(2^4)$ is constructed as $K[x]$ modulo $1 + x^3 + x^4$ and $\beta$ is the class of $x$, so ...
1
vote
0answers
674 views

Generator and char. polynomial for a binary Galois Field produced by an external-XOR LFSR

My question is regarding LFSRs (Linear Feedback Shift Registers), and the binary Galois Field produced by them (also commonly termed GF($2^n$) ). I understand that a given n-bit LFSR produces a ...
8
votes
3answers
6k views

Addition and multiplication in a Galois Field

I am attempting to generate QR codes on an extremely limited embedded platform. Everything in the specification seems fairly straightforward except for generating the error correction codewords. I ...