0
votes
0answers
25 views

Studying a code in cryptography

So,i'm given a binary code $C$ with it's generator matrix $G=(A,B)$ where $A,B$ are given matrices. The task is to study the code. First question: What does this form $(A,B)$ mean? how would $G$ look ...
0
votes
1answer
35 views

Periodic streams

I have problems proving the following result; Suppose you have two periodic streams $x_n$ with period $M$ and $y_n$ with period $N$. The streams $x_n+y_n$ and $x_n y_n$ are periodic with periods ...
3
votes
0answers
183 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
1answer
52 views

Determine the number of divisors in $K[x]$ of $1 + x^{15}$ and of $1+x^{120}$

where $K[x]$ is the set of all polynomials where coefficients are elements of $K$ $(0,1)$ Is this related to the problem of finding how many cyclic linear codes there are if $n = 15$ and $120$? I've ...
1
vote
2answers
155 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 ...
0
votes
1answer
66 views

showing a code exists given the lower bound of its dimension (with respect to its length and distance)

How do I show that there exists a code $C$ of length $n$ and distance at least $d$ such that $ max_{length(C) = n, d(C) \geq d} \mid C\mid \geq \frac{2^n}{\binom{n}{0} + \binom{n}{1} + ...
1
vote
2answers
125 views

Checking if a linear code exists - singleton , hamming and gilbert-varshamov bounds do not help.

Suppose I want to check if a (11, 6, 4) code exists. I cannot prove non-existence using the singleton and the hamming bound. I also cannot prove existence using the gilbert-varshamov bound. I'm not ...
4
votes
1answer
184 views

Combinatory + Coding Theory

I am reading about an algorithm for finding minimum-weight words in large linear codes. Let $c$ be the codeword of weight $w$ to recover (with size $n$ and in $GF(2)$). Let $N = \left\{1, 2, \ldots, ...
0
votes
1answer
143 views

Markov Chain + Decoding algorithm

I am ready a paper Canteaut and Chabaud, I don't get understand the values of transition matrix $P$, in the Proposition 4. If, anybody read this paper please help me understand this values: $P_{u,u}$, ...
1
vote
1answer
39 views

What is a memoryless nonlinear boolean function?

I have been reading about shift register based keystream generators in cryptography. One usual method of generating keystream sequences is feeding the output of several Linear Feedback Shift Registers ...
2
votes
0answers
69 views

(Please check working) Given RSA encoding function $E: x\to x^{11} \pmod{3737}$ find the decoding function $D$

Please check the working and final answer to the question: Question: Given RSA encoding function $E: x\to x^{11} \pmod{3737}$ find the decoding function $D$ My working: $\phi(3737) = \phi(37) \times ...
1
vote
1answer
256 views

Generator matrices of codes

I need a little help please. The Klein curve $X\subset \mathbb{P}^{2} $ given by homogeneous equation: $x^{3}y+y^{3}z+z^{3}x=0$. Show that the space $L(m(z))$ is generated by elements of the form ...
1
vote
1answer
260 views

Linear Code in Cryptography

Is it possible to construct a [6,2] linear code that is two-error correcting? I think I need to use this Theorem: Suppose that C is a t-error correcting code in (Z_2)^8. Then order(C)*((n choose ...
1
vote
1answer
131 views

Error Correcting Codes

Let $C$ be the two-error correcting code: $\{(00000000),(11100011),(00011111),(11111100)\}$ in $(Z_2)^8$. Then it says to find two vectors that are correctable to a codeword in $C$ (of bit length ...
7
votes
2answers
1k views

Is the set of all finite sequences of letters of Latin alphabet countable/uncountable? How to prove either?

Today in Coding/Cryptography class, we were talking about basic definitions, and the professor mentioned that for a set $A=\left \{ \left. a, b, \dots, z \right \} \right.$ (the alphabet) we can ...