# Questions tagged [coding-theory]

Coding theory studies the properties of codes and their fitness for specific applications, and typically involves the removal of redundancy and the detection and/or correction of errors in transmitted data.

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### Current mathematics theory used in cryptography/coding theory

What are the mainstream techniques borrowed from algebraic geometry (or some other branch of mathematics) which are currently used in cryptography/coding theory? I've only heard about a small subset ...
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### Does there exist a proof-of-retrievability scheme that is publicly-verifiable, limited-use, and does not use homomorphic encryption?

I find myself wanting to test out a practical implementation of a proof-of-retrievability scheme, simply out of curiosity. These schemes seem to be divided into two variations, publicly-verified and ...
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### RS Erasure Coding and Shamir's Secret Sharing

So I was trying to understand the basic difference between erasure coding and secret sharing, and I found this paper (that you can find here or here). For what I understand, it states that Shamir's ...
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### Can error correction and detection be done without adding extra bits?

I have gone through error detection and correction techniques like Hamming codes, and BCH codes require extra parity bits for detection and correction. While sending data, we always seem to introduce ...
2k views

### How to hash similar strings to the same hash value?

Suppose that $s_1$ and $s_2$ are two stings that have a small hamming distance. Is there a preimage resistant "hash" function ($H$) that can map them to the same value i.e., $H(s_1) = H(s_2)$?
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### Why doesn't “Classic McEliece” need scrambling?

The original McEliece scheme uses two random matrices S and P to scramble the generator matrix and uses $\mathsf S·\mathsf G·\mathsf P$ as the public key. The Niederreiter variant also does about the ...
707 views

### What does this notation stand for when describing a code?

This code has appeared in some online course material. I understand the $(5, 4, 3)$ refers to (length, num codewords, distance) but no explanation of the $Z_2^5$ notation is given: One $(5,4,3)$ ...
343 views

### Hermitian curves introductory references

Could you give me some reference to start on Hermitian Curves. Some papers or textbooks would be perfect, and please mention if it's math inclined or comp.sci. inclined. I've only seen hermitian ...
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### Implementing the Mceliece Encryption - making the Generator Matrix

I am working on an implementation of the Mceliece Encryption system (MCE) and the Niederreiter encryption system. I have been through the basics of finite fields, polynomial arithmetic and some coding ...
397 views

### Where can I find useful data for cryptography/coding theory?

When implementing cryptographic/coding theory algorithms one need to use data like big prime numbers, numbers in $Z_n$ and their inverses, irreducible polynomials in $Z_n[x]$ and so on... While ...
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### Words having weight near to minimum distance

I am studying the NP-Problem of the codes Syndrome Decoding. The formulation is show below. Input: a binary matrix $H$ of dimension $r \times n$ and a bit string $S$ of length $r$. Property: there ...
278 views

### About using mistakes as part of a code

Could a code be developed where one uses intentional errors say in english, as a text to encode? For example someone might have a message 'Agent X must report to station 5'. This could be distorted ...
122 views

### Traitor tracing - codeword properties

Let $c ≥ 2$. A code $C ⊂ Q^n$ is a $c$-frameproof code if for any set $X ⊂ C$ with $|X| ≤ c$ we have desc$(X) ∩ C = X$. Thus the only codewords that a coalition of up to $c$ pirates is capable of ...
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### Choosing the Bernoulli distribution for LPN encryption scheme

The symmetric-key encryption scheme from [1] is based on the LPN (learning parity with noise) problem. The definition of the problem is, informally, that the adversary cannot recover $\mathbf{s}$ from ...
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### Unique decoding Radius in Reed Solomon Codes

In one of the coding theory books I read the unique decoding radius for Reed Solomon codes is $\frac{1-\rho}{2}$. Precisely, if the relative distance be less than these amount so the receiver is able ...
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### Need an example to write permutation in cycle notation [closed]

Actually, I don't quite understand the question. What does $a_{i,j}$ means? Is it the element in the matrix from row i and column j? Can anyone give me an example? Better use another matrix because I ...
### Value of $t$ in Fuzzy Exractor
Is there a defined method to choose value of $t$ when using fuzzy extractor to reconcile two close secrets? I did try with multiple values ranging from 5 to close to half of the sequence. I ...