Questions tagged [hamming-distance]

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MDS codes with a given proportion of weights

I was trying to understand the hamming weight distribution of codewords in MDS codes. I read (https://wiki.cse.buffalo.edu/cse545/content/mds-codes) the following: Let C be a $[n, k, d]$ MDS code . ...
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Hamming code distance and error detection

Suppose that data are transmitted in blocks of sizes 1000 bits. What is the maximum error rate under which error detection and retransmission mechanism (1 parity bit per block) is better than using ...
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21 views

Covering radius of a code in the Hamming space

A deterministic $(2−2/(k+1))^n$ algorithm for $k$-SAT based on local search  I have read this paper and I couldn't understand how to culculate the $covering$ $radius$ of a code in the Hamming space. ...
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96 views

Find binary number with max hamming distance wrt given set of binary numbers

Suppose we have a set $A$ of binary numbers with the same length $n$. For example (with $n=8$): $A = \{ 10010011, 01011011, 00010010, 11110001\}$ Now, I want to find the binary number $z$ (also with ...
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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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143 views

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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54 views

Minimum number of strings to cover entire space within Hamming distance

Given $(n, k)$: What is the minimum number $x$ of (binary) strings such that all $n$-bit (binary) strings are within $k$ Hamming distance of some string? Is there an asymptotic expansion or lower ...