1
vote
1answer
29 views

Hamming Code (9,5): Is my Parity Check correct?

I have an exercise about designing parity checks for the Hamming (9,5) group code with minimum distance $3$. I use the following notation for the generator matrix: $$ ...
2
votes
3answers
100 views

Finding element in binary representation of $GF(2^6)$

I got the following task: Let $F = GF(2^6 )$ be K[x] modulo the primitive polynomial $h(x) = 1 +x ^2 +x ^3 +x ^5 +x ^6$ , and let $\alpha$ be the class of x. I have a table with the binary ...
1
vote
2answers
386 views

Why should we append zeros during CRC calculation?

Say we have M as message bits , why do we need to append r-zeros to M message bits before performing the division to obtain r-bit checksum. Why don't we directly perform the division on the M message ...
1
vote
1answer
226 views

What is the average Levenshtein distance between two random binary strings of length $L$?

For example, for length $L=7$, two random binary strings might be: 0100101 1010011 The Levenshtein distance here would be 5, as it would require 5 bit-flips to ...
3
votes
2answers
76 views

Recognize a valid binary Golay codeword

Are there any properties of a binary [24,12,8] Golay code which would allow me to say, for example, that a given 24-bit word is or is not a Golay codeword for some generator matrix? That is to say, is ...
1
vote
1answer
137 views

Problem about BCH code

I have another homework to do, please give me some hints in order to solve this problem: "Determine whether the dual of an arbitrary BCH code is a BCH code."
1
vote
1answer
192 views

Problem about narrow sense BCH-Code

I have an homework to do and i have no idea where to start. The question is: "Show that a narrow-sense binary BCH-code of length $ n=2^m-1 $ and designed distance $ 2t+1 $ has minimum distance $ 2t+1 ...
4
votes
1answer
244 views

A question dealing with residual codes.

I've been reading about residual codes, and have come across several statements that I am having trouble showing. (1.) By using the residual code, one can show that a $[16, 5, 8]$ binary code ...
3
votes
0answers
205 views

An Upper Bound for an $[n,k,d]$ Linear Binary Code.

I've been reading about the various upper bounds for different types of codes. Recently, I came across a statement that is similar to the Singleton Upper Bound that I am having trouble proving. The ...
4
votes
1answer
75 views

Proving that $A_2(13,7) = 8$

It is not too difficult to find a binary code consisting of $8$ words, each $13$ bits long, keeping the distance between every pair of words at least $7$. I know it is not possible to find $9$ words ...
3
votes
1answer
64 views

q-ary code/Latin squares

For any value of $q$ the largest number of elements in any q-ary code $C$ of length $4$, distance $3$ is $q^2$. How can we prove that this is attainable iff there are a pair of mutually orthogonal ...
3
votes
1answer
6k views

Calculating CRC by long division: How to decide the top number of long division?

Ok, I know how to use long division by using regular numbers, but when comes to binary numbers I'm getting confused. In following calculation I can see the equation solved but I don't understand ...