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Questions tagged [hamming-code]

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when can i detect the position of error in hamming code

I have 4-bit data with the hamming code 0010011. the parity parameters are: p1=0 , p2=0 , p3=0 and the check codes are: ...
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finding the overhead and distance of an unknown code based on message making algorithm

for an information word M with m bits that is coded as following: M is coded into a word A using an unknown code that allows detection of not more than one error. the code word is the word obtained ...
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Trouble understanding theory for error detection and correction in repetition code

Question 1 Consider a repetition code to detect $m$ errors. What is the smallest repetition parameter $k$ (i.e., the number of repetitions per bit) it should be used so that the code can always ...
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Huffman Coding vs Arithmetic Coding

Are there conditions under which given text $T$ that huffman code and arithmetic code will produce the exact encoding of $T$?
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How does this answer for automata and Hamming distance not lead to inconsistencies?

I had already been given the answer by the TA in class, but I don't understand it. I'm not asking for the answer on a homework problem or anything. The problem: The Hamming distance ("distance") of ...
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1answer
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How can I correct this Hamming code?

I'm trying to decode the following Hamming sequence (using EVEN parity and knowing there is a 1-bit error), which contains an ASCII value: 01100110101 I've tried ...
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81 views

Incorrect Answer Trying to Find Hamming Distance

A 010101 B 110011 C 111000 D 000111 The minimum Hamming distance of those code words is 3 as the minimum difference is 3 but the correct answer is 2. How can I ...
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Hamming code extension with additional parity bit

Let $Ham$ be the $[7,4,3]_2$ Hamming code. It is known that $\{w(c):c\in Ham\}\subseteq\{0,3,4,7\}$, where $w(c)$ is the Hamming weight of the word $c$. A code $C$ of length $n$ is called cyclic if ...
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Minimum Hamming Distance of code for ASCII strings

I couldn't figure out how to answer the following question: Suppose we want to transmit a string of 3 ASCII characters, and in order to be able to detect or correct the message, we append the sum of ...
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1answer
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Binary code and Hamming distance

I'm learning about CRC and Hamming distance and I have three questions. Lets say we have binary code described by ($+$ refers to sum modulo $2$): \begin{alignat*}{1} a_1 &+ a_2 &+ a_3 &+ ...
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In the Hamming code, how many control bits are needed to be able to correct an error in 15-bits transmited

i don't know if right answer is 4 or 5 ! what did you understand from this question if it was a QCM ? thanks
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1answer
588 views

Hamming distance and parity

For an Hamming code of $n$ bit there are $k$ bit reserved for the data and $p$ bit for the parity where $p$ is the minimum integer for which the following inequation is satisfied: $$2^p \geqslant p + ...
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Ultrametric Binary States

All metric spaces obey the triangle inequality which is, for three points $a,b,c$, that $$d(a,c) \le d(a,b) + d(b,c)$$ One interesting special case of a metric space is one endowed with an ...
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Computing Hamming Distance Between Binary Vectors

Consider the following problem: Input: We are given a set $S$ of $n$ binary vectors. A binary vector is of the form $(b_0, b_1, ... b_n)$, where $b_i \in \{0, 1\}$. Therefore, there are $n$ vectors ...
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Rearranging strings so that the Hamming distance between them is 1

This is a question from CodeFights.com: Given an array of equal-length strings, check if it is possible to rearrange the strings in such a way that after the rearrangement the strings at ...
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LDPC:How to detect total number of errors in a codeword using minimum distance?

Currently, i working with LDPC for FPGA implementation. I have formed H matrix of size 102X204 (N=204,K=102,M=102,R=0.5). Doubt in Error detection and correction for bigger matrix. I know that code'...
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266 views

How to count the bits with a 1 bit error correction Hamming code?

I've seen both ways of counting the bits when determining where to place the parity bits in a 1 bit error correction Hamming code. Some people count the bits starting from the left, others do it by ...
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Find hamming codewords in r=2^k dimensions

There is the original problem, and an equivalent problem. The equivalent problem: construct a set $A$ that contains bit arrays of length $r-1$, where $|A|=2^{r-1}/r$ and $hamming \space distance (i, ...
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1answer
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Lower limit on the number of check bits needed to correct single errors

I was going through Andrew S. Tannenbaum's computer networks book, and on page 206 of it, he has derived the number of check bits needed to correct single bit errors. The derivation goes as follows: ...
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1answer
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Gray-like code with maximum value <= maximum value of original symbol

I want to iterate through the numbers $0,1,2,\dots,n-1$ in some order, where each number in the sequence differs by only one bit from the previous bit. I'm going to be using each number as an index ...
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Minimum hamming distance of multiple binary words

Our task is to compute the minimum hamming distance for the following 16-bit words: ...
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1answer
383 views

What is the reason behind a specific ordering of the rows in the generator matrix for Hamming codes?

What order the rows are in a Hamming generator matrix are irrelevant for the Hamming coding to work, given the check matrix is built accoridngly. In order to limit cognitive overload, it could have ...
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115 views

Cyclic Redundancy Check Codewords Finding the Original Message

So I have the received transmitted message in polynomial form as $$T'(X) = X^{15}+X^{13}+X^8+X^7+X^4+X^3$$ and the error polynomial as $$E(X) = X^{16}+X^{13}+X^3$$ and the generator polynomial as ...
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How to pick Hamming distance

Wikipedia's article Cyclic redundancy check states that for the same n (bits) there are multiple CRCs possible with different polynomial. Then it lists this Best CRC Polynomials article that gives ...
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coding theory- perfect codes

I'm new to stackoverflow so please bear with me. A tutorial question I got given was as follows: You are given that $C \subseteq D \subseteq F^n_q$ where $|C| < |D|$ and $C$ is a perfect code. ...
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Hamming code — identical parity bits for different errors

(7,4) Hamming Code (HC) detects all 2-bit errors and corrects all 1-bit errors. However, there can be 2-, 3- or 4-bit errors that come with the same parity bits as that of 1-bit errors. Eg.: Let ...
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use of Hamming Distance in Communication Networks

I am trying to put things in places on the use of Hamming Distance (HD) in error detection and correction in Computer Networks. I'm looking for correction/verification on the following: HD is a ...
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1answer
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Hamming error correction with non-uniform error correction capability

If I understood correctly, Hamming codes assume the uniform correction among all the bits. This means all the bits have the same weight in terms of correction. Are there any error correcting codes ...
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280 views

Hamming and BCH codes

Why are Hamming codes the best 1-error-correcting codes? I need references. I know that hamming codes are the best 1-error-correcting codes but I want to know why they are best?
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1answer
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Compute the Hamming code with odd parity for the memory word 1101 1001 0001 1011

This is the problem I have: Compute the Hamming code with odd parity for the memory word 1101 1001 0001 1011 (2 pts.). In your solution, mark the parity bits as in the following example, where ...