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Volume 22, No 1, 2015, P. 32-50 UDC 519.8
Keywords: perfect code, Hamming code, nonsystematic code, affine nonsystematic code, affine 3-nonsystematic code, component. DOI: 10.17377/daio.2015.22.438 Sergey A. Malyugin1 Received 26 January 2014 References[1] S. V. Avgustinovich and F. I. Solov’eva, On nonsystematic perfect binary codes, Probl. Peredachi Inf., 32, No. 3, 47–50, 1996. Translated in Probl. Inf. Transm., 32, No. 3, 47–50, 1996.[2] S. A. Malyugin, On enumeration of the perfect binary codes of length 15, Diskretn. Anal. Issled. Oper., Ser. 2, 6, No. 2, 48–73, 1999. Translated in Diskrete Appl. Math., 135, No. 1–3, 161–181, 2004. [3] S. A. Malyugin, Nonsystematic perfect binary codes, Diskretn. Anal. Issled. Oper., Ser. 1, 8, No. 1, 55–76, 2001. [4] S. A. Malyugin, On affine nonsystematic codes, Proc. Conf. Devoted to the 90th Anniversary of A.A. Lyapunov, Novosibirsk, Russia, Oct. 8–11, 2001, pp. 393–394, Novosibirsk, 2009. Available at http://www.sbras.ru/ws/Lyap2001/2288/. Accessed Jan. 13, 2015. [5] S. A. Malyugin, On enumeration of nonequivalent perfect binary codes of length 15 and rank 15, Diskretn. Anal. Issled. Oper., Ser. 1, 13, No. 1, 77–98, 2006. Translated in J. Appl. Ind. Math.,1, No. 1, 77–80, 2007. [6] S. A. Malyugin, Affine nonsystematic codes, Diskretn. Anal. Issled. Oper., 19, No. 4, 73–85, 2012. Translated in J. Appl. Ind. Math.,6, No. 4, 451–459, 2012. [7] S. A. Malyugin, Affine 3-nonsystematic codes, Diskretn. Anal. Issled. Oper., 21, No. 4, 54–61, 2014. Translated in J. Appl. Ind. Math., 8, No. 4, 552–556, 2014. [8] A. M. Romanov, On construction of perfect nonlinear binary codes by symbol inversion, Diskretn. Anal. Issled. Oper., Ser. 1, 4, No. 1, 46–52, 1997. [9.] A. M. Romanov, On nonsystematic perfect codes of length 15, Diskretn. Anal. Issled. Oper., Ser. 1, 4, No. 4, 75–78, 1997. Translated in Discrete Appl. Math., 135, No. 1–3, 255–258, 2004. [10] K. T. Phelps and M. LeVan, Kernels of nonlinear Hamming codes, Des. Codes Cryptogr., 6, No. 3, 247–257, 1995. [11] K. T. Phelps and M. LeVan, Nonsystematic perfect codes, SIAM J. Discrete Math., 12, No.1, 27–34, 1999. [12] F. I. Solov’eva, Switchings and perfect codes, in I. Alth¨ofer et al., eds., Numbers, Information and Complexity, pp. 311–324, Kluwer Acad. Publ., Dordrecht, 2000. |
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