Search results
Results from the WOW.Com Content Network
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 ternary Golay code consists of 3 6 = 729 codewords. Its parity check matrix is [].Any two different codewords differ in at least 5 positions. Every ternary word of length 11 has a Hamming distance of at most 2 from exactly one codeword.
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 >, then it is of one of the following four types: [1]
Indirect parity measurements coincide with the typical way we think of parity measurement as described above, by measuring an ancilla qubit to determine the parity of the input bits. Direct parity measurements differ from the previous type in that a common mode with the parities coupled to the qubits is measured, without the need for an ancilla ...
where H is the parity-check matrix of the Hamming code and is given by = []. The [[,,]] Steane code is the first in the family of ...
LDPC codes and MDPC are based on the same component code: the parity checksum, and in my opinion the relationship stop there. In an LDPC codes, the number of symbols involved in a parity check is small and does not depend on the length of the code, while in MDPC the number of symbols involved in one parity check depend on the length of the code.
The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.
Alice generates a (n − k) × n parity check matrix, H, for the code, G. Alice selects a random (n − k) × (n − k) binary non-singular matrix, S. Alice selects a random n × n permutation matrix, P. Alice computes the (n − k) × n matrix, H pub = SHP. Alice's public key is (H pub, t); her private key is (S, H, P).