{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T08:51:04Z","timestamp":1767084664843,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T00:00:00Z","timestamp":1736726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper investigates the features of using modified Hamming codes, which are also known as Hsiao codes. Self-checking digital devices are proposed to be implemented with calculations testing using two diagnostic signs. These signs indicate that the functions (there are functions that describe check bits) belong to the class of self-dual Boolean functions and also belong to the codewords of Hsiao codes (these are codes with an odd column of weights). The authors have established that all check functions can be self-dual for a certain number of the Hsiao codes\u2019 data symbols. Such codes can be used in the synthesis of concurrent error-detection circuits by two diagnostic signs. The paper describes the structure of an organization for a concurrent error-detection circuit based on Hsiao codes with self-dual check functions. Some experimental results are presented on the synthesis of self-checking devices using the proposed methodology. The controllability of the structure and the number of test combinations both increased. Hsiao codes can be effectively used with self-dual check functions in the synthesis of self-checking digital devices.<\/jats:p>","DOI":"10.3390\/computation13010015","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T09:49:17Z","timestamp":1736761757000},"page":"15","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Combinational Circuits Testing Based on Hsiao Codes with Self-Dual Check Functions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4563-6411","authenticated-orcid":false,"given":"Dmitry V.","family":"Efanov","sequence":"first","affiliation":[{"name":"Higher School of Transport, Institute of Machinery, Materials and Transport, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia"},{"name":"\u00abAutomation and Remote Control\u00bb Department, Tashkent State Transport University, Tashkent 100167, Uzbekistan"},{"name":"\u201cAutomation, Remote Control and Communication on Railway Transport\u201d Department, Russian University of Transport, Moscow 127994, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9171-234X","authenticated-orcid":false,"given":"Tatiana S.","family":"Pogodina","sequence":"additional","affiliation":[{"name":"Higher School of Transport, Institute of Machinery, Materials and Transport, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia"}]},{"given":"Nazirjan M.","family":"Aripov","sequence":"additional","affiliation":[{"name":"\u00abAutomation and Remote Control\u00bb Department, Tashkent State Transport University, Tashkent 100167, Uzbekistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7289-7820","authenticated-orcid":false,"given":"Sunnatillo T.","family":"Boltayev","sequence":"additional","affiliation":[{"name":"\u00abAutomation and Remote Control\u00bb Department, Tashkent State Transport University, Tashkent 100167, Uzbekistan"}]},{"given":"Asadulla R.","family":"Azizov","sequence":"additional","affiliation":[{"name":"\u00abAutomation and Remote Control\u00bb Department, Tashkent State Transport University, Tashkent 100167, Uzbekistan"}]},{"given":"Elnara K.","family":"Ametova","sequence":"additional","affiliation":[{"name":"\u00abAutomation and Remote Control\u00bb Department, Tashkent State Transport University, Tashkent 100167, Uzbekistan"}]},{"given":"Feruza F.","family":"Shakirova","sequence":"additional","affiliation":[{"name":"\u00abAutomation and Remote Control\u00bb Department, Tashkent State Transport University, Tashkent 100167, Uzbekistan"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,13]]},"reference":[{"key":"ref_1","first-page":"1085","article-title":"Methods for Providing Safety in Discrete Systems","volume":"55","author":"Gavzov","year":"1994","journal-title":"Autom. 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