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07:29
A new tag was created by user193319.
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Q: Uniform Probability Measure on a Finitely Generated Group

user193319I am working through a proof. Here's the setup: $\Gamma$ is a finitely generated group with finite symmetric generating set $S \subset \Gamma$. In this proof the author takes an arbitrary "uniform probability measure $\mu$ on $S$." First, how does one construct this measure $\mu$? And does it ext...

07:51
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Q: How to find minimum Hamming distance of concatenated two encoded words?

Yos Given data word $M$ of $2n$ bits $M$ is split into 2 words $M_1M_2$ whereas the length of $M_1$ is $n$ bits as well as the length of $M_2$ is also $n$ bits. $M_1$ and $M_2$ are encoded separately using Hamming code and result in words $K_1$ and $K_2$ respectively. The final result is the conca...

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Q: Does Cyclic Redundancy Check result in more extra bits overhead than Hamming code?

Yos For a data word of $16$ bits which is the most correct claim: Hamming code extra bits overhead will be greater than CRC because Hamming code corrects one error while CRC can only detect errors. CRC extra bits overhead is greater because Hamming code uses minimal number of bits for en...

1
Q: What is the minimal Hamming distance of $x$-error detecting code and $y$-error correcting code?

Yos What is the minimal Hamming distance of $12$-error detecting code and $8$-error correcting code? We know that a code is said to be $x$ error detecting if, and only if, the minimum Hamming distance between any two of its codewords is at least $x+1$ ($13$ in our case). In addition a code is $y$-e...

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Q: What is the minimal Hamming distance of concatenation of some word and a part of it encoded using Hamming codes?

Yos A word $M$ is of $n^2$ bits, $n>3$ is arranged in a $n\times n$ matrix. $A$ is the main diagonal of the matrix (that is elements $a_{i,j}$, $i=j$) and is encoded with Hamming code, resulting in $B$. The final result transmitted is word $M$ concatenated with $B$ (let us call it $R$). What is the ...

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4 hours later…
11:47
I don't think Hamming codes deserve their own tag even though they are nice. — Jyrki Lahtonen 3 hours ago

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