# Questions tagged [error-correcting-codes]

Error correcting codes are used to transmit information through a noisy channel. They also have applications in theoretical computer science and combinatorics. Some well known error correcting codes are Hamming codes, Reed–Solomon codes, and Reed–Muller codes.

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### Undetectable error correcting codes

I have a 256 bit string (indistinguishable from random) which I wish to encode into a greater length string using an error correction code. The result must also be indistinguishable from random. It ...
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### How to read Nasa Convolutional code?

Here is a picture from Andrew S. Tanenbaum, Computer Networks, 5th edition, Chapter 3 (The data link layer), Page 207(English Version)/Page 206(Japanese Version): I want to verify whether my ...
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### Effects of parity bit on odd code length regarding its size after alternation

I am trying to understand code distance, but I am not sure regarding the following scenario: Assume that you have an information word M with m bits, that You code into a coding word using the ...
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### Upper bound on size of minimal binary coverage code

Let $1 \le r \le n$ b e integer(with $n$ large) and let $\mathscr X_n$ be the set set of all $2^n$ binary strings of length $n$. A binary $r$-coverage code is a subset $S$ of $\mathscr X_n$ such that ...
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### Calculate number of error-correcting code check bits

To design a code with $m$ data bits and $r$ check bits which allow all single-bit errors to be corrected, the formula $$(n + 1) 2^m \leq 2^n$$ with $n = m + r$ and $(m + r + 1) \leq 2^r$ is used. Why ...
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### Error correction code without error detection

Error detection and correction codes require many bits of redundancy for correcting even a modest number of erroneous bits. However, we often have out-of-band methods to determine when and where the ...
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### Decoding cyclic code, assuming we have no errors

Assuming the coded data is errorless and given generator polynomial coefficients. By what algorithm can I decode the data coded by matrix constructed by given generator polynomial?
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### How can I correct this Hamming code?

I'm trying to decode the following Hamming sequence (using EVEN parity and knowing there is a 1-bit error), which contains an ASCII value: 01100110101 I've tried ...
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### Improving heading measurements from low cost compass module

I have heading measurements of two Sensors (BNO055 and HMC6343) and also accurate measurements from better sensors for comparison from a rotating platform. Most of the measurements are with some kind ...
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### Difference between CRC and Hamming Code

I am a bit confused on the difference between Cyclic Redundancy Check and Hamming Code. Both add a check value attached based on the some arithmetic operation of the bits in the message being ...
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### How to handle generator polynomial in CRC if given in (x+1) (x^3+ x^2 +1) form?

I am trying to find the frame check sequence in cyclic redundancy check(CRC). Given that the generator polynomial is $\ g(x)= (x+1)(x^3 + x^2 + 1)$. Let's say the data sequence is $\ 10110001$. In ...
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### What is the motivation for the defining smooth locally decodable codes?

I am interested to understand why smooth locally decodable codes were defined historically as they were (I believe it may be because they make for easier analysis in obtaining lower bounds on locally ...
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### In the Hamming code, how many control bits are needed to be able to correct an error in 15-bits transmited

i don't know if right answer is 4 or 5 ! what did you understand from this question if it was a QCM ? thanks
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### Bit errors and hamming distance

I'm trying to learn for my exam and had the following practice question: Take a code with the following code words. 101100010111 110001001001 101110111011 Errors of how many bits can be corrected? ...
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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, ...
### 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,...