# Questions tagged [coding-theory]

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

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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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### What's the decoding time complexity of LT codes?

LT codes are practical fountain codes that are near-optimal erasure correcting codes. Simply stated, for encoding a $n$-block message, each packet first chooses a degree $d\in\{1,\ldots,n\}$ ...
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### How to construct a random error-correcting code (its generator matrix) according to the code parameters?

I need to construct a random code which corrects T errors, has R check bits and has N maximum bits in the transmitting word. I have researched the topic and found a few theorems about the bounds (The ...
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### Is arithmetic coding restricted to powers of $2$ in denominator equivalent to Huffman coding?

With restriction to $\frac{k}{2^n}$ as line segment ends, does arithmetic coding degrade to Huffman coding? As far as I can tell, each symbol will be encoded with an integer amount of bits, which is ...
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### finding amount of errors that can be fixed based on code length [closed]

i tried to look online and search this site and others but haven't found any good explanation to the following simple question: how many errors can a code with length k(k>2)fix?
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### distance of a code name in scheme

i wonder: is it true that if we take a information word, call it M(with m bits) for example, and code it by first coding M using a code, that we don't know anything about, except of it a length of k, ...
54 views

### Complexity of nearest codeword in cyclic codes

Is it $NP$-complete given $c(x),g(x)\in\mathbb{F}_2[x]$ where $g$ generates a cyclic code of length $n$ (so $g\mid x^n-1$), and $\deg c<n$ to find the nearest codeword to $c$? This is related to ...
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### Optimal prefix-free binary code with several codewords already assigned

The classic Huffman algorithm, as Wikipedia states, finds an optimal prefix-free binary code with minimum expected codewords length, given a set of symbols and their weights. Now, suppose codewords ...
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### Where can I find someone that will sit with me and explain the analytics reports from my iPhone and computer? [closed]

This may seem like a dumb question to most people, BUT PLEASE READ THIS!! I AM BEYOND DESPERATE to get rid of a hacker that is digitally stalking me and terrorizing me. I picked your forum because ...
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### MDS codes with a given proportion of weights

I was trying to understand the hamming weight distribution of codewords in MDS codes. I read (https://wiki.cse.buffalo.edu/cse545/content/mds-codes) the following: Let C be a $[n, k, d]$ MDS code . ...
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### Which algorithm to detect errors in 32bit data with 8bit parity

I want to transmit a 32bit message in eight groups of 5bit each. This leaves me with 8bits to use for error checking. Overall, a group is likely transmitted without error, but when there is an error ...
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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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### using 2 short CRC(s) VS one longer CRC

I'm doing some research on the CRCs, but i can't find informations about the use of two (or more) short CRCs compared to the use of a longer CRC: Suppose that i have a dataword A of some length and 3 ...
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### Is there a database of linear codes with “small” covering radius

Does anyone keep a database of (or including) linear codes with small covering radius? I'm specifically interested in the smallest-dimension codes known of covering radius R ($2\le R \le 4$ say) for ...
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### Simplification of Sum of Hamming Weight Sets

Let $k,n,K,m \in \mathbb{N}$ such that $k<n$. Let $l\in \mathbb{R}$, such that $0 \leq l \leq 1$. I am analyzing an algorithm and I need $O(N)$. Could you help me with the reduction of the ...
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### Parameters of a linear code

Consider the code $C=\{c=(c_1...c_n): c \in \Bbb F_q^n, c_1=c_n\} \subset \Bbb F_q^n$. I was able to prove that the code is a linear code because it is closed under addition and scalar multiplication....
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### Conditions to apply Source Coding Theorem

I was wondering what are the conditions to apply source coding theorem (SCT). 1. Is it applied only to uniform-length coding, what about variable-length coding, does it also satisfy SCT? I was ...
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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, ...