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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22
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7answers
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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 ...
11
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3answers
3k views

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 ...
11
votes
2answers
2k views

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 ...
3
votes
0answers
129 views

Solving LPN using algorithm for syndrome decoding

Given an algorithm $A_D$ which solves an instance of the decoding problem $e \in \mathbb{F}_2^n$ in time $T_D$ given a parity check matrix $H \in \mathbb{F}_2^{(n-k)\times n}$ and a syndrome $s \in \...
3
votes
1answer
85 views

Question about block erasure codes

I have a question about linear block erasure codes that are described in this paper. I briefly describe the idea behind the linear erasure codes and then I ask my question. Given a set $d=\langle x_i ...
1
vote
1answer
78 views

Traitor tracing - determining a set of codewords

I am reading some notes and having trouble understanding the following example: Let $F$ be a finite set of size $q$, where $q ≥ 2$. Let $n$ be an integer, where $n ≥ 2$. For a subset $X ⊆ F^n$ of ...