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In a polynomial code over () with code length and generator polynomial () of degree , there will be exactly code words. Indeed, by definition, p ( x ) {\displaystyle p(x)} is a code word if and only if it is of the form p ( x ) = g ( x ) ⋅ q ( x ) {\displaystyle p(x)=g(x)\cdot q(x)} , where q ( x ) {\displaystyle q(x)} (the quotient ) is of ...
A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
The algorithm attempts to find the same word, but in all its word endings. A fuzzy search will match a different word. Words (but not phrases) accept approximate string matching or "fuzzy search". A tilde ~ character is appended for this "sounds like" search. The other word must differ by no more than two letters. Not the first two letters.
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix.This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
A Diceware word list is any list of 6 5 = 7 776 unique words, preferably ones the user will find easy to spell and to remember. The contents of the word list do not have to be protected or concealed in any way, as the security of a Diceware passphrase is in the number of words selected, and the number of words each selected word could be taken ...
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Function calls and blocks of code, such as code contained within a loop, are often replaced by a one-line natural language sentence. Depending on the writer, pseudocode may therefore vary widely in style, from a near-exact imitation of a real programming language at one extreme, to a description approaching formatted prose at the other.