# Questions tagged [coding-theory]

The theory of error-correcting codes stems from Shannon's 1948 _A mathematical theory of communication_, and from Hamming's 1950 "Error detecting and error correcting codes".

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### On sparse $0/1$ linear equations solvable with compressed sensing

If you have a system of $m$ linearly independent equations in $n$ variables with domain $0/1$ and we know there is at least one solution with at most $d$ variables to be $1$ then if $m$ at least a ...
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### Algorithm for constacyclic codes

I am asking if there is a decoding algorithm for the constacyclic codes. I know many decoding algorithm for cyclic codes but i didn't found any result
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### Embedding a binary subspace to $l_2$ in a much lower dimension

I'm trying to find a way to embed a binary linear subspace of dimension $n$ (a linear code) to the Euclidian space while reducing the dimension significantly. The subspace (or code) contains points ...
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### When can this condition on linear codes be satisfied?

It would be useful to me to have a result of the following kind (which I would need to generalize, but this case is already interesting). Let $r<n$ be positive integers and let $\delta>0$ be a ...
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### Strategy of Responder in Rényi Ulam Liar Games

I tried posting this in Math Stack Exchange but got no responses, so I figured I could try my luck here. My main concern is that I can't figure out how to get started on my "research" (bear with me, I'...
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### $\left< 15\right>^7/15$-womcode construction

In the article Womcodes constructed with projective geometries Frans Merkx constructed several good wom-codes (write-once memory codes, see How to reuse a "write-once" memory by Rivest & Shamir ...
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### Is there a Kolmogorov complexity proof of the prime number theorem?

Lance Fortnow uses Kolmorogov complexity to prove an Almost Prime Number Theorem (https://lance.fortnow.com/papers/files/kaikoura.pdf, after theorem $2.1$): the $i$th prime is at most $i(\log i)^2$. ...
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### Optimal Encoding of Sets with DeBruijn-likeSequences

A DeBruijn sequences of order $n$ encodes all possible strings of length $n$ over an alphabet with $k$ symbols and algorithms for their construction are well known among those familiar with the ...