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English version: Journal of Applied and Industrial Mathematics, 2017, 11:2, 227235 

Volume 24, No 2, 2017, P. 5367 UDC 519.8
Keywords: perfect binary code, Hamming code, Vasil’ev code, component, continuum, hypercontinuum. DOI: 10.17377/daio.2017.24.535 Serguey A. Malyugin ^{1} Received 31 March 2016
References[1] S. V. Avgustinovich and F. I. Solov’eva, Construction of perfect binary codes by sequential shifts of αcomponents, Probl. Peredachi Inf., 33, No. 3, 15–21, 1997 [Russian]. Translated in Probl. Inf. Transm., 33, No. 3, 202–207, 1997.[2] Yu. L. Vasil’ev, On nongroup closepacked codes, in A. A. Lyapunov, ed., Problemy kibernetiki (Problems of Cybernetics), Vol. 8, pp. 337–339, Fizmatgiz, Moscow, 1962 [Russian]. [3] 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 [Russian]. Translated in Discrete Appl. Math., 135, No. 1–3, 161–181, 2004. [4] S. A. Malyugin, Nonsystematic perfect binary codes, Diskretn. Anal. Issled. Oper., Ser. 1, 8, No. 1, 55–76, 2001 [Russian]. [5] S. A. Malyugin, Perfect binary codes of infinite length, Prikl. Diskretn. Mat., Prilozh., No. 8, 117–120, 2015 [Russian]. [6] V. N. Potapov, Infinitedimensional quasigroups of finite orders, Mat. Zametki, 93, No. 3, 457–465, 2013 [Russian]. Translated in Math. Notes, 93, No. 3, 479–486, 2013. [7] 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 [Russian]. [8] K. T. Phelps and M. LeVan, Kernels of nonlinear Hamming codes, Des. Codes Cryptogr., 6, No. 3, 247–257, 1995. [9] F. I. Solov’eva, Switchings and perfect codes, in I. Althöfer et al., eds., Numbers, Information and Complexity, pp. 311–324, Kluwer Acad. Publ., Dordrecht, 2000. 

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