We consider dynamic and online variants of 2D pattern matching between an m×m pattern and an n× n text. All the algorithms we give are randomised and give correct outputs with at least constant probability. – For dynamic 2D exact matching where updates change individual symbols in the text, we show updates can be performed in O(log n) time and queries in O(log m) time. – We then consider a mode...

In this paper, we propose the minimal joint Hamming weight conversion for any binary expansions of d integers. With redundant representations, we may represent a number by many expansions, and the minimal joint Hamming weight conversion is the algorithm to select the expansion that has the least joint Hamming weight. As the computation time of the cryptosystem strongly depends on the joint Hamm...

Given a satisfiable 3-SAT formula, how hard is it to find an assignment to the variables that has Hamming distance at most n/2 to a satisfying assignment? More generally, consider any polynomial-time verifier for any NP-complete language. A d(n)-Hammingapproximation algorithm for the verifier is one that, given any member x of the language, outputs in polynomial time a string a with Hamming dis...

We consider the problem of defining and evaluating the Hamming distance between two– dimensional pattern P [1..m, 1..m] of pixels and two–dimensional text T [1..n, 1..n] of pixels when also rotations of P are allowed. In particular, we are interested in the orientation and location of P that gives the minimum Hamming distance. The number of different orientations for P is O(m3) when the center ...

Received Nov 21, 2017 Revised Jan 26, 2018 Accepted Feb 12, 2018 In the OFDM communication system channel encoder and decoder is the part of the architecture. OFDM channel is mostly affected by Additive White Gaussian Noise (AWGN) in which bit flipping of original information leads to fault transmission in the channel. To overcome this problem by using hamming code for error detection and corre...

The results presented in this paper are parts of my doctoral thesis [ 193; the algorithm and some of the characterizations in Section 7 have been introduced in [ 181. Motivation for isometric embeddings into Hamming graphs has come from communication theory (Graham and Pollak [ 121) an-d linguistics (Firsov 1181). Isometric subgraphs of Hamming graphs also appear in biology as “quasi-species” (...

We present an extension of the pairwise Hamming distance, the r-wise Hamming distance, and show that it can be used to fully characterize the maximum-likelihood decoding (MLD) error of an arbitrary code used over the binary erasure channel (BEC). Based on these insights, we present a new design criterion for a code: the minimum r-wise Hamming distance. We prove that, for every r ≥ 2, the class ...

The $r$ -th generalized Hamming metric and the notation="LaTeX">$b$ -symbol are two different generalizations of metric. former is used on wire-tap channel Type II, latter motivated by limitations reading process in high-density data ...