Abstract. A new principle of modification of codes with summation of on-bits that allows to expand the class of modified codes and obtain codes with better characteristics of low multiplicity error detection is proposed. An overview of known methods of classical codes modifications with summation of individual information bits is presented. A method of constructing modified codes with summation, based on determination of the smallest nonnegative deduction weight incomplete information vector and control of "unused" information bits by using the correction coefficient, which is a convolution modulo two is described; in particular, the correction factor may include discharge, subject to a deduction of the weight. All the possible ways of constructing error-correcting codes modified with the summation are considered. Characteristics of error detection in the information vectors of these codes are analyzed.  The conditions, under which a code with summation detects the maximal number of double errors in the information vectors and the conditions under which the code will have the minimum number of monotone non-detectable errors are established. The presented principle of codes modification is shown to allow for increasing the number of well-known codes used in technical diagnostics of discrete systems.

Keywords: technical diagnostics, code summation, Berger code, modified Berger code, improved error detection ability

References:

1. Parkhomenko P.P., Sogomonyan E.S. Osnovy tekhnicheskoy diagnostiki. Optimizatsiya algoritmov diagnostirovaniya, apparaturnye sredstva (Basics of technical diagnostics. Optimization of Algorithms of Diagnosing, Hardware Means), Moscow, 1981, 320 р. (in Russ.)
2. Sapozhnikov V.V., Sapozhnikov Vl.V., Khristov Kh.A., Gavzov D.V.Metody postroeniya bezopasnykh mikroelektronnykh sistem zheleznodorozhnoy avtomatiki(Methods of Creation of Safe Microelectronic Systems of Railway Automatic Equipment), Moscow,1995, 272 р. (in Russ.)
3. Ubar R., Raik J., Vierhaus H.-T. Design and Test Technology for Dependable Systems-on-Chip (Premier Reference Source), Hershey, NY, IGI Global, 2011, 578 p.
4. Lisenkov V.M., Bestem'yanov P.F., Leushin V.B., Lisenkov A.V., Van'shin A.E. Sistemy upravleniya dvizheniem poezdov na peregonakh (Control Systems of Train Service on Stages), Moscow,2009, 324 р. (in Russ.)
5. Sapozhnikov Vl.V., Kononov V.A., Kurenkov S.A., Lykov A.A., Nasedkin O.A., Nikitin A.B., Prokof'ev A.A., Tryasov M.S. Mikroprotsessornye sistemy tsentralizatsii (Microprocessor Systems of Centralization), Moscow, 2008, 398 р. (in Russ.)
6. Rao T.R., Fujiwara E. Error Control Coding for Computer Systems, NY, Prentice Hall, 1989, 584 p.
7. Sogomonyan E.S., Slabakov E.V. Samoproveryaemye ustroystva i otkazoustoychivye sistemy (The Self-Checked Devices and Failure-Safe Systems), Moscow, 1989, 208 р. (in Russ.)
8. Nicolaidis M., ZorianY.J. of Electronic Testing: Theory and Application, 1998, no. 1–2(12), рр. 7–20. DOI: 10.1023/A:1008244815697.
9. Mitra S., McCluskey E.J. Proc. of Intern. Test Conf., Atlantic City, NJ, 3–5 Oct. 2000, рр. 985–994.
10. Piestrak S.J. Design of Self-Testing Checkers for Unidirectional Error Detecting Codes, Wrocław, Oficyna Wydawnicza Politechniki Wrocłavskiej, 1995, 111 p.
11. Mourad S., McCluskey E.J.IEEE Transact. on Industrial Electronics, 1989, no. 2(36), рр. 254–262. DOI: 10.1109/41.19077.
12. Ghosh S., Basu S., Touba N.A. Proc. of the 23rd IEEE VLSI Test Symp. (VTS'05), 2005,рр. 315–320.
13. Fujiwara E. Code Design for Dependable Systems: Theory and Practical Applications, New Jersey, John Wiley & Sons, 2006, 720 p.
14. Aksenova G.P. Problemy Upravleniya, 2008, no. 5, рр. 62–66. (in Russ.)
15. Berger J.M.Information and Control, 1961, no. 1(4), рр.68–73. DOI: 10.1016/S0019-9958(61)80037-5.
16. Freiman C.V. Information and Control, 1962, no. 1(5), рр. 64–71. DOI: 10.1016/S0019-9958(62)90223-1.
17. Blyudov A., Efanov D., Sapozhnikov V., Sapozhnikov Vl. Proc. of the 10th IEEE East-West Design & Test Symp. (EWDTS`2012), Kharkov, Ukraine, 14–17 Sept., 2012, рр. 114–117. DOI 10.1109/EWDTS.2013.6673150.
18. Blyudov A.A., Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Electronic Modeling, 2012, no. 6(34), рр. 17–29.(in Russ.)
19. Efanov D., Sapozhnikov V., Sapozhnikov Vl., Blyudov A.Proc. of the 11th IEEE East-West Design & Test Symposium (EWDTS`2013), Rostov-on-Don, Russia, 27–30 Sept., 2013, рр. 261–266. DOI 10.1109/EWDTS.2013.6673133.
20. Blyudov A.A., Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2013, no. 6, рр. 153–164. (in Russ.)
21. Blyudov A.A., Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V.Automation and Remote Control, 2014, no. 8, рр.131–145.(in Russ.)
22. Marouf M.A., Friedman A.D. Proc. of the 8th Annual Intern. Conf. on Fault-Tolerant Computing, Toulouse, France, 1978, рр. 179–183.
23. Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2010, no. 6, рр. 155–162.(in Russ.)
24. Bose B., Lin D. J. IEEE Transact. on Computers, 1985, no. C–34, рр.1026–1032.
25. Sapozhnikov V., Sapozhnikov Vl., Efanov D. Proc. of the 13th IEEE East-West Design & Test Symposium(EWDTS`2015), Batumi, Georgia, 26–29 Sept., 2015, рр. 181–187.DOI 10.1109/EWDTS.2015.7493133.
26. Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2015, no. 10, рр. 152–169. (in Russ.)
27. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V., Cherepanova M.R. Electronic Modeling, 2016, no. 2(38), рр. 27–48. (in Russ.)
28. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V., Cherepanova M.R. Electronic Modeling, 2016, no. 3(38), рр.47–61. (in Russ.)
29. Blyudov A.A., Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2012, no. 1, рр. 169–177. (in Russ.)
30. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Automation on transport, 2015, no. 1(1), pp. 84–107. (in Russ.)