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Problemy Peredachi Informatsii, 1969, Volume 5, Issue 4, Pages 19–27
(Mi ppi1818)
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Nonbinary Arithmetic Correcting Codes
V. M. Gritsenko
Abstract:
A method is considered for synthesizing arithmetic separable codes with error correction in one position for nonbinary positional systems of calculation. To construct the codes the theory of second-degree congruences is used in conjunction with the elements of group theory. Theorems are given for determining the various $r$-ary codes analytically. The relation between $r$-ary and $r^s$-ary codes is used to construct codes with correction of groups of errors in the $r$-ary system of calculation. A number of modules are found which generate correcting codes for calculation systems with bases $r=3,4,\dots,10,16$.
Received: 12.04.1968 Revised: 16.05.1969
Citation:
V. M. Gritsenko, “Nonbinary Arithmetic Correcting Codes”, Probl. Peredachi Inf., 5:4 (1969), 19–27; Problems Inform. Transmission, 5:4 (1969), 15–22
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https://www.mathnet.ru/eng/ppi1818 https://www.mathnet.ru/eng/ppi/v5/i4/p19
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Abstract page: | 497 | Full-text PDF : | 161 |
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