Geodesic
Coding information by Walsh matrices
Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 121-124.

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The representation of the general linear group $\mathrm{GL}(n, 2) $ by the automorphism subgroup $\mathrm{GL}(N, 2) $ under the multiplicative notation in its action in the space $ \mathbb{R} ^ N $, where $ N = 2 ^ n $, is considered. Each matrix as an element of the group $\mathrm{GL}(n, 2) $ defines ordering: the group $ \mathbb{Z}_2 ^ n $ and its group of characters, which are popular in digital processing of information in the form of discrete Walsh functions. On the basis of the fast Walsh transform and this correspondence the authors created a software prototype of an automatic output signal coding system. The essence of the proposed software product is the number of possible permutations, which is calculated by the formula $(2^n-2^0)(2^n-2^1)\ldots (2^n-2^{n-1})$ for $n$-th order matrices. Based on the program, it is possible to organize a multi-channel system of reconfigurable decoders when transmitting hidden information over open communication channels.
Keywords: discrete Walsh functions, fast Walsh transform, Kronecker product.
Mots-clés : code matrix 
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     title = {Coding information by {Walsh} matrices},
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     publisher = {mathdoc},
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     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2020_13_a35/}
}
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M. S. Bespalov; K. M. Malkova. Coding information by Walsh matrices. Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 121-124. http://geodesic.mathdoc.fr/item/PDMA_2020_13_a35/

[1] Malozemov V. N., Masharskii S. M., Osnovy diskretnogo garmonicheskogo analiza, Lan, SPb., 2012

[2] Zalmanzon L. A., Preobrazovanie Fure, Uolsha, Khaara i ikh primenenie v upravlenii, svyazi i drugikh oblastyakh, Nauka, M., 1989

[3] Bespalov M. S., “Sobstvennye podprostranstva diskretnogo preobrazovaniya Uolsha”, Problemy peredachi informatsii, 46:3 (2010), 60–79 | MR | Zbl

[4] Morris S., Dvoistvennost Pontryagina i stroenie lokalno kompaktnykh abelevykh grupp, Mir, M., 1980

[5] Trakhman A. M., Trakhman V. A., Osnovy teorii diskretnykh signalov na konechnykh intervalakh, Sov. radio, M., 1975

[6] Bespalov M. S., Sklyarenko V. A., Diskretnye funktsii Uolsha i ikh prilozheniya, VlGU, Vladimir, 2014

[7] Bespalov M. S., “Novaya numeratsiya matrits Uolsha”, Problemy peredachi informatsii, 45:4 (2009), 43–53 | MR | Zbl

[8] Piterson U., Ueldon E., Kody, ispravlyayuschie oshibki, Mir, M., 1976

[9] Bespalov M. S., “Diskretnoe preobrazovanie Krestensona”, Problemy peredachi informatsii, 46:4 (2010), 91–115 | MR | Zbl