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Results tagged with coding-theory
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user 4720
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".
6
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Accepted
Multiplication by polynomials x^2+1 ; x^2+x+1. Does minimal Hamming norm of image equal to 5 ?
Yes. Without loss of generality, we can assume $p(x)$ is not divisible by $x$. Then $p(x)(x^2+1)$ and $p(x)(x^2+x+1)$ both have constant term $1$, so the combined Hamming weight is at least $4$ from …
- 16.8k
20
votes
Accepted
covering by spherical caps
There exist coverings such that each point is covered at most $400 d \log d$ times, and you can improve this bound a little if you look at the covering density, i.e., the average number of times each …
- 16.8k