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Questions tagged [coding-theory]

The study of data representations that enable error detection, error correction and/or compression.

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9 votes
4 answers
3k views

No compression algorithm can compress all input messages?

I just started reading a book called Introduction to Data Compression, by Guy E. Blelloch. On page one, he states: The truth is that if any one message is shortened by an algorithm, then some other ...
Jack M's user avatar
  • 264
14 votes
5 answers
3k views

PRNG for generating numbers with n set bits exactly

I'm currently writing some code to generate binary data. I specifically need to generate 64-bit numbers with a given number of set bits; more precisely, the procedure should take some $0 < n < ...
Koz Ross's user avatar
  • 813
4 votes
1 answer
39k views

Hamming distance required for error detection and correction

I have already asked a pair of questions on the hamming distance, hamming code, valid and invalid codewords on this website, because I cannot understand those concepts fully, and in a few weeks or ...
user avatar
61 votes
8 answers
34k views

Is Morse code without spaces uniquely decipherable?

Are all Morse code strings uniquely decipherable? Without the spaces, ......-...-..---.-----.-..-..-.. could be Hello World ...
john mangual's user avatar
  • 1,951
7 votes
1 answer
200 views

Prove fingerprinting

Let $a \neq b$ be two integers from the interval $[1, 2^n].$ Let $p$ be a random prime with $ 1 \le p \le n^c.$ Prove that $$\text{Pr}_{p \in \mathsf{Primes}}\{a \equiv b \pmod{p}\} \le c \ln(n)/(n^{...
user1374864's user avatar
-1 votes
1 answer
126 views

A max-even subset problem

I want to know if there is any polynomial algorithm for the problem, or any NP-completeness result. Given a set $S$ and $m$ subsets $C_1, \dots, C_m$ of $S$, we want to find a non-empty set $X\...
MohammadJavad Hajialikhani's user avatar
3 votes
2 answers
5k views

How to decode multiple-digit gamma codes and get the gap sequence?

How to decode gamma code ($\gamma$ code): 1110001110101011111101101111011 and get the gap sequence? Detailed information about Gamma codes ($\gamma$ codes) ...
Mike's user avatar
  • 149
3 votes
1 answer
2k views

Compute minimum hamming distance of a code

How do you find the minimum hamming distance of a code? A naive way is computing the distance of each pair of codewords in our code. It becomes hard when the code is sufficiently large. Is there a ...
SuperStamp's user avatar
0 votes
0 answers
35 views

How to decode multiple-digit gamma codes and get the gap sequence? [duplicate]

How to decode gamma code ($\gamma$ code): 1110001110101011111101101111011 and get the gap sequence? Detailed information about Gamma codes ($\gamma$ codes) ...
Mike's user avatar
  • 149