Search results
Results from the WOW.Com Content Network
The ability to code a stimulus two different ways increases the chance of remembering that item compared to if the stimulus was only coded one way. There has been controversy to the limitations of the dual-coding theory. Dual-coding theory does not take into account the possibility of cognition being mediated by something other than words and ...
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]
A self-dual code is one which is its own dual. This implies that n is even and dim C = n /2. If a self-dual code is such that each codeword's weight is a multiple of some constant c > 1 {\displaystyle c>1} , then it is of one of the following four types: [ 1 ]
This triple repetition code is a Hamming code with m = 2, since there are two parity bits, and 2 2 − 2 − 1 = 1 data bit. Such codes cannot correctly repair all errors, however. In our example, if the channel flips two bits and the receiver gets 001, the system will detect the error, but conclude that the original bit is 0, which is incorrect.
Allan Paivio's dual-coding theory is a basis of picture superiority effect. Paivio claims that pictures have advantages over words with regards to coding and retrieval of stored memory because pictures are coded more easily and can be retrieved from symbolic mode, while the dual coding process using words is more difficult for both coding and retrieval.
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method. Let α be a primitive element of GF(q m).
The Reed–Solomon code is a [n, k, n − k + 1] code; in other words, it is a linear block code of length n (over F) with dimension k and minimum Hamming distance = + The Reed–Solomon code is optimal in the sense that the minimum distance has the maximum value possible for a linear code of size ( n , k ); this is known as the Singleton bound .
A code is defined to be equidistant if and only if there exists some constant d such that the distance between any two of the code's distinct codewords is equal to d. [4] In 1984 Arrigo Bonisoli determined the structure of linear one-weight codes over finite fields and proved that every equidistant linear code is a sequence of dual Hamming ...