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Since the Hamming distance between "000" and "111" is 3, and those comprise the entire set of codewords in the code, the minimum Hamming distance is 3, which satisfies 2k+1 = 3. Thus a code with minimum Hamming distance d between its codewords can detect at most d-1 errors and can correct ⌊(d-1)/2⌋ errors.
Personal identification number. A personal identification number ( PIN ), or sometimes redundantly a PIN number or PIN code, is a numeric (sometimes alpha-numeric) passcode used in the process of authenticating a user accessing a system. The PIN has been the key to facilitating the private data exchange between different data-processing centers ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...
A Postal Index Number ( PIN; sometimes redundantly a PIN code) [note 1] refers to a six-digit code in the Indian postal code system used by India Post. On 15 August 2022, the PIN system celebrated its 50th anniversary.
A postal code (also known locally in various English-speaking countries throughout the world as a postcode, post code, PIN or ZIP Code) is a series of letters or digits or both, sometimes including spaces or punctuation, included in a postal address for the purpose of sorting mail . As of August 2021, the Universal Postal Union lists 160 ...
Postal codes used in the United Kingdom, British Overseas Territories and Crown dependencies are known as postcodes (originally, postal codes). They are alphanumeric and were adopted nationally between 11 October 1959 and 1974, having been devised by the General Post Office ( Royal Mail ). [2]
A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space where is the finite field with q elements. Such a code is called a q -ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords.
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