# Tag Info

## Hot answers tagged hamming-distance

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### Largest set of 10-digit numbers where none have Hamming Distance = 1 with any other

There is a simple solution: use exactly the strings with sums of digits being divisible by $10$. There are $10^9$ such strings and it is easy to enumerate them, find $i$-th of them in the ...
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### What is the intuition behind working of hamming codes

Hamming codes are designed to correct a single error. A valid codeword $p_1 p_2 m_3 p_4 m_5 m_6 m_7$ satisfies the constraints \begin{align} &p_1 \oplus m_3 \oplus m_5 \oplus m_7 = 0 \\ &p_2 \...
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### Number of binary words that form a group of Hamming weight at most d

Your structure is known as a group anticode with maximal distance $d$. The obvious construction is to take all vectors of the form $(x_1,\ldots,x_d,0,\ldots,0)$, obtaining a group of size $2^d$. ...
• 278k
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### Hierarchial clustering cannonnical representation?

You can always adjust your algorithm to use a deterministic tie-breaking rule, e.g., sort the data points before applying the clustering algorithm, and always break ties in favor of the earliest/...
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### How to recognise the number of errors that can be detected and corrected of a large set of codewords (k) each having a specified number of bits (n)?

There are $2^{10}$ binary strings of length $10$. We can partition them into pairs $x_1\ldots x_90,x_1\ldots x_91$. Since your code contains more than $2^9$ codewords, it will contain at least one ...
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### Calculate number of error-correcting code check bits

Consider a binary code $C$ of length $n$ (each codeword consists of $n$ bits), containing $2^m$ codewords, and allowing all single-bit errors to be corrected. Let $x \in C$, and let $B_x$ denote all ...
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### Hamming code distance and error detection

Let's see. With parity, each block is 1001 bits long vs 1010 bit for Hamming code. So if the error rate is 0, then you economize 9 bits. OTOH, if each second block fails, the in 50% of cases you will ...
• 1,898
1 vote
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### Covering radius of a code in the Hamming space

It's easier to remove from your table all lines with codes already in C. In your case only two lines will remain, minimum distance in both lines are 1, so the maximum distance of these two is ...
• 1,898
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### Polynomial generator required to detect single bit error in Cyclic Redundancy Check codes

You just need to concentrate on the polynomial division here. First consider the case where we need to detect one - bit error . For this case $e(x) = x^k$ we can choose any polynomial with terms >...

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