# Questions tagged [coding-theory]

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

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### Is Morse code without spaces uniquely decipherable?

Are all Morse code strings uniquely decipherable? Without the spaces, ......-...-..---.-----.-..-..-.. could be Hello World ...
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### Is Morse Code binary, ternary or quinary?

I am reading the book: "Code: The Hidden Language of Computer Hardware and Software" and in Chapter 2 author says: Morse code is said to be a binary (literally meaning two by two) code ...
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### Hamming code -- identical parity bits for different errors

(7,4) Hamming Code (HC) detects all 2-bit errors and corrects all 1-bit errors. However, there can be 2-, 3- or 4-bit errors that come with the same parity bits as that of 1-bit errors. Eg.: Let ...
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### How is the Varshamov-Tenegolts code decoded?

For $0 \leq a \leq n$ the VT code $VT_a(n)$ consists of all tuples $(x_1,x_2,..,x_n) \in \{ 0,1\}^n$ such that $\sum_{i=1}^{n} ix_i = a (mod (n+1))$ For example $VT_0(4) = \{ 0000,1001,0110,1111 \}$ ...
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### About codes over $\mathbb{F}_2$

I was looking through these notes but I am not sure I can locate the answer to these questions of mine - it would be great if someone can just even point out what to look for! So any set of binary ...
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### How many independent yes/no questions can be asked about a point in binary space (linear vs nonlinear codes)?

This question springs from thinking about the potential benefits of using nonlinear codes instead of linear codes. Say we have a point $x \in \{0,1\}^k$ and we want to guess what it is. A naive scheme ...
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### Error-correction code for transmission only with bit-flipping from 0 to 1

I am using a transmission system that uses a Bloom filter (this part is out of my control). I want to send a small amount of data (32 bits) using this system. For each bit [0,31], I add its index to ...
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### Lexicographical position of a string in its type class

I have the following problem: Given a string $x\in\{1,...,M\}^+$ of length $n$. Let $S$ be the set of all words with exactly the same numbers of occurences of smybols as in $x$. In fact, $S$ consists ...
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### 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 ...
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### Is there a fundamental difference in LIFO and FIFO entropy coding?

The top two competing entropy coders at the moment are Arithmetic Coding (AC) and Asymmetrical Number Systems (ANS). A very interesting difference between the two is that AC is FIFO and ANS is LIFO. ...
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### What's the error-correcting capacity (randomly errors, or burst errors) of polar code?

Polar codes, invented by Arikan, with low encoding and decoding complexity. But the minimum distance of polar codes is not great. The normalized minimum distance goes to 0 with the block size. Yet, ...
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### What is the error-detection-probability of CRC

I have a table which stores all serial numbers of devices in my system: ...
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### Showing that a binary linear code $C$ is self-dual

Let $C*$ be the length 8 binary code obtained by adding a parity check symbol to each word in $C$. (so a word $c_1, c_2, c_3, c_4, c_5, c_6, c_7$ is extended to the word \$c_1, c_2, c_3, c_4, c_5, c_6,...
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