Very fast method to find hamming distance between two Strings of equal length...
I have a private class that I want to be able to find the shortest Hamming Distance between two Strings of equal length in Java. The private class holds a char[] and contains a method to compare...
View ArticleExplicit, small resolving sets for Hamming graphs
Definition. Let $ G = (V;E)$ be a finite, undirected graph. $ R = \{r_1, \ldots, r_k \} \subseteq V$ . $ R$ resolves $ G$ if $ $ V \to [0, \infty]^k, v \mapsto (d_G(v,r_1), \ldots, d_G(v, r_k)) $ $ is...
View ArticlePrimes with given Hamming weight
If I understand correctly, in the following MO-thread Are There Primes of Every Hamming Weight? two users of the site claim that it has been already proven that, for every sufficiently large $ n \in...
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Covering radius of a code in the Hamming sace
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...
View ArticleHamming 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...
View ArticleMost likely error with hamming distance
I have a basic question about hamming distances, something confuse me in the book I’m reading about it. Let’s assume we have a codeword $ y$ that received an error $ e$ . Thus we had the following...
View ArticleHamming connectivity of regular languages
Call a language $ L$ Hamming connected iff, for every pair of strings $ x, y \in L^2$ , where $ |x|=|y|$ , $ x$ may be transformed into $ y$ by a sequence of single symbol in-place replacements, so...
View ArticleDecoding bit streams using Hamming Code
I want to decode the following bit stream using Hamming code: 01110110 Once using even parity and once odd parity. I will show my work. For even parity: $ p_{1} \; p_{2} \; 0 \; p_{3} \; 1 \; 1 \; 1...
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Are My Answers to This Hamming Code Example Correct?
I have attempted to answer this question on Hamming code but i am very new to it and would appreciate feedback on my answers, Thank you! Question My Answers The post Are My Answers to This Hamming...
View ArticleLargest set of 10-digit numbers where none have Hamming Distance = 1 with any...
I’m working on a system that will require manual data entry of 10-digit numbers (Σ = 0123456789). To help prevent data errors, I want to avoid generating any two strings that have a hamming distance...
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