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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.).
Compared to randomly generated LDPC codes, structured LDPC codes—such as the LDPC code used in the DVB-S2 standard—can have simpler and therefore lower-cost hardware—in particular, codes constructed such that the H matrix is a circulant matrix.
In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics. [1] These codes are named in honor of Marcel J. E. Golay whose 1949 paper [2] introducing ...
Matrix groups. If n is some positive integer, we can consider the set of all invertible n by n matrices with real number components, say. This is a group with matrix multiplication as the operation. It is called the general linear group, and denoted GL n (R) or GL(n, R) (where R is the set of real numbers).
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Group codes can be constructed by special generator matrices which resemble generator matrices of linear block codes except that the elements of those matrices are endomorphisms of the group instead of symbols from the code's alphabet. For example, considering the generator matrix
Parity-check matrix. In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms.
Guilded is a competitor of Discord and primarily focuses on video game communities, such as those focused on competitive gaming and esports. [1] [3] It provides features intended for video gaming clans, such as scheduling tools and integrated calendars. [3] [4] Guilded is developed by Guilded, Inc. which has been an independent product group of the Roblox Corporation since August 16, 2021. [5] [6]