biorthogonal decomposition
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2021 ◽  
pp. 101-119
Author(s):  
D. V. Litichevskiy ◽  

The existence of a biorthogonal decomposition of the space V of dimension n over the field GF(q) is constructively proved, namely, two representations of it are obtained as direct sums of subspaces V = W0⊕W1⊕. . .⊕WJ⊕VJ and V = W˜0⊕W˜1⊕. . .⊕W˜J⊕V˜J ,such that at the j-th level of the decomposition, for 0 < j 6 J, Vj−1 = Vj⊕Wj , V˜j−1 == V˜j ⊕ W˜j , the subspace Vj is orthogonal to W˜j , and the subspace Wj is orthogonal to V˜j . The partition of the space at the j-th level is made with the help of pairs of level filters (hj, gj) and (h˜j, g˜j), for the construction of which the corresponding algorithms have been developed and theoretically proved. A new family of biorthogonal wavelet codes is built on the basis of the multilevel wavelet decomposition scheme with coding rate 2−L, where L is the number of used decomposition levels, and examples of such codes are given.


2014 ◽  
Vol 57 (2) ◽  
pp. 025005 ◽  
Author(s):  
B Ph van Milligen ◽  
E Sánchez ◽  
A Alonso ◽  
M A Pedrosa ◽  
C Hidalgo ◽  
...  

2014 ◽  
Vol 56 (11) ◽  
pp. 114012 ◽  
Author(s):  
C Galperti ◽  
C Marchetto ◽  
E Alessi ◽  
D Minelli ◽  
M Mosconi ◽  
...  

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