A. Liu. Two applications of a Hamming code. The Col- lege Mathematics Journal, 40(1), 2009.Liu, A. (2009). Two Applications of a Hamming Code. The Mathematical Association of America, 40(1) 2-5.A. Liu, "Two applications of a Hamming code," The College Mathe- matics Journal, vol. 40, no. 1, 2009.
A particularly interesting class of self-dual codes is those of Type II which have high minimum distance (called extremal or near-extremal). It is notable that this class of codes contains famous unique codes: the extended Hamming code, the extended Golay code, and the extended quadratic ...
Here is the implementation of Hamming distance: Pseudo Code: Read the first string, ‘strOne’, and the second string, 'strTwo', from the user. If the length of ‘strOne’ is not equal to the length of ‘strTwo’, throw an exception. Initialize a variable 'distance' to 0. Loop throu...
Standardly, a Hamming code is applied with distance greater than 3 (sure number of checking bits has to be added to each 32-bit word) which involves SEC-DED at minimum (a single error correction and double error detection within a single word). Some STM32 microcontrollers use parity bit (...
The dual code of C, denoted by C⊥, is defined to be C⊥={x∈F2n:∑i=1nxici=0∀c∈C} and is an [n,n−k,d⊥] binary linear code, where d⊥ is the Hamming distance of C⊥. We say that C is self-orthogonal if C⊆C⊥ and C is projective if d⊥≥3. One of the...
Appendix 1: How to Decode the Hamming (7,4) Code As mentioned earlier, the decoders essentially perform the inverse function of the coders. Although such tasks can be fairly straightforward, they are not always obvious. To illustrate, let us look at how a channel decoder would decode the ...
To select a value forminpts, consider a value greater than or equal to the number of dimensions of the input data plus one [1]. For example, for ann-by-pmatrixX, set'minpts'equal top+1 or greater. One possible strategy for selecting a value forepsilonis to generate ak-distance graph...
To further enhance the performance of low-rate sparse codes, generalized LDPC (GLDPC) codes are introduced, which replaces the single parity-check (SPC) code constraints by constraints based on algebraic codes, e.g., Hamming codes [23] and Hadamard codes [24]. The powerful algebraic code ...
We let dH(C) denote the minimum Hamming distance of the code C. A code C of length n over Fq with the minimum Hamming distance dH(C) is called an (n,|C|,dH(C))q code. If C is a linear code, then it is called an [n,k,dH(C)]q code, where k is the dimension of C....
To select a value forminpts, consider a value greater than or equal to the number of dimensions of the input data plus one [1]. For example, for ann-by-pmatrixX, set'minpts'equal top+1 or greater. One possible strategy for selecting a value forepsilonis to generate ak-distance graph...