01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date:
15.08.1952
Keywords:
coding theory,
combinatorics.
Subject:
I am interested in the theory of perfect codes. I have suggested several constructions of perfect codes by concatenation and switching (jointly with S. V. Avgustinovich). The following nontrivial properties of perfect binary codes are investigated. It was suggested the method of $\alpha$-components to construct perfect codes, the class of nonsystematic perfect codes was discovered jointly with S. V. Avgustinovich. The automorphism group of perfect codes; the metrical rigidity of $q$-ary codes close to perfect codes by close-packed properties; rank-kernel problem for perfect codes are investigated (jointly with different coworkers).
Biography
1969–1974 — student of Jakutsk State University University (YaSU), 1974–1977 — assistant of professor of University, 1977–2002 — post-graduate student, then junior, then (since 1990) senior of Novosibirsk Institute of Mathematics of Siberian Branch of Russian Academy of Sciences. Graduated from Faculty of Mathematics Yakutsk in 1974 (department of algebra and analitical geometry). Ph. D. thesis was defended in 1990. A list of my works contains more than 100 titles. Since 1990 I have delivered lectures on the special graduate course "Coding Theory" and have led together seminars for the following graduate courses: "Methods on Discrete mathematics", "Introduction in Discrete mathematics", jointly with S. V. Avgustinovich the research seminar "Coding Theory". Doctor Science Defence was at 2008.
Main publications:
Solov'eva F. I. Switchings and perfect codes // Numbers, information and complexity. Dordrecht: Kluwer Acad. Publ., 2000, 311–314.
Solov'eva F. I. Structure of $i$-components of perfect binary codes, Discrete Appl. Math., 2001, 111(1,2), 189–197.
Solov'eva F. I., Avgustinovich S. V., Lobstein A. Intersection, matrices for partitions by binary perfect codes // IEEE Trans. Inform. Theory, 2001, 47(4), 1621–1624.
I. Yu. Mogil'nykh, F. I. Solov'eva, “On weight distributions for a class of codes with parameters of Reed–Muller codes”, Probl. Peredachi Inf., 58:3 (2022), 33–44
I. Yu. Mogilnykh, F. I. Solov'eva, “On bases of BCH codes with designed distance $3$ and their extensions”, Probl. Peredachi Inf., 56:4 (2020), 10–18; Problems Inform. Transmission, 56:4 (2020), 309–316
I. Yu. Mogilnykh, F. I. Solov'eva, “Coordinate transitivity of a class of extended perfect codes and their SQS”, Sib. Èlektron. Mat. Izv., 17 (2020), 1451–1462
I. Yu. Mogilnykh, F. I. Solov'eva, “A concatenation construction for propelinear perfect codes from regular subgroups of $\mathrm{GA}(r,2)$”, Sib. Èlektron. Mat. Izv., 16 (2019), 1689–1702
F. I. Solov'eva, “On transitive uniform partitions of $F^n$ into binary Hamming codes”, Sib. Èlektron. Mat. Izv., 16 (2019), 886–892
2017
10.
I. Yu. Mogilnykh, F. I. Solov'eva, “Propelinear codes related to some classes of optimal codes”, Probl. Peredachi Inf., 53:3 (2017), 54–63; Problems Inform. Transmission, 53:3 (2017), 251–259
I. Yu. Mogilnykh, F. I. Solov'eva, “On the symmetry group of the Mollard code”, Probl. Peredachi Inf., 52:3 (2016), 73–83; Problems Inform. Transmission, 52:3 (2016), 265–275
I. Yu. Mogilnykh, F. I. Solov'eva, “On a class of perfect codes with maximum components”, Sib. Èlektron. Mat. Izv., 13 (2016), 645–655
2015
13.
I. Yu. Mogilnykh, F. I. Solov'eva, “On separability of the classes of homogeneous and transitive perfect binary codes”, Probl. Peredachi Inf., 51:2 (2015), 57–66; Problems Inform. Transmission, 51:2 (2015), 139–147
G. K. Guskov, F. I. Solov'eva, “On extremely transitive extended perfect codes”, Diskretn. Anal. Issled. Oper., 20:5 (2013), 31–44; J. Appl. Industr. Math., 8:1 (2014), 53–62
15.
D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small ranks and extended perfect binary codes”, Diskretn. Anal. Issled. Oper., 20:4 (2013), 46–64; J. Appl. Industr. Math., 7:4 (2013), 522–536
D. I. Kovalevskaya, F. I. Solov'eva, E. S. Filimonova, “Steiner triple systems of small rank embedded into perfect binary codes”, Diskretn. Anal. Issled. Oper., 20:3 (2013), 3–25; J. Appl. Industr. Math., 7:3 (2013), 380–395
D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small rank embedded into extended perfect binary codes”, Diskretn. Anal. Issled. Oper., 19:5 (2012), 47–62; J. Appl. Industr. Math., 7:1 (2013), 68–77
F. I. Solov'eva, G. K. Guskov, “On construction of vertex-transitive partitions of $n$-cube into perfect codes”, Diskretn. Anal. Issled. Oper., 17:3 (2010), 84–100
F. I. Solov'eva, A. V. Los', “On partitions into perfect $q$-ary codes”, Diskretn. Anal. Issled. Oper., 16:3 (2009), 63–73; J. Appl. Industr. Math., 4:1 (2010), 136–142
F. I. Solov'eva, “On transitive partitions of an $n$-cube into codes”, Probl. Peredachi Inf., 45:1 (2009), 27–35; Problems Inform. Transmission, 45:1 (2009), 23–31
F. I. Solov'eva, N. N. Tokareva, “Distance regularity of Kerdock codes”, Sibirsk. Mat. Zh., 49:3 (2008), 668–681; Siberian Math. J., 49:3 (2008), 539–548
F. I. Solov'eva, A. V. Los', “Intersections of $q$-ary perfect codes”, Sibirsk. Mat. Zh., 49:2 (2008), 464–474; Siberian Math. J., 49:2 (2008), 375–382
S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “Partitions of an $n$-Cube into Nonequivalent Perfect Codes”, Probl. Peredachi Inf., 43:4 (2007), 45–50; Problems Inform. Transmission, 43:4 (2007), 310–315
F. I. Solov'eva, N. N. Tokareva, “On distance nonregularity of Preparata codes”, Sibirsk. Mat. Zh., 48:2 (2007), 408–416; Siberian Math. J., 48:2 (2007), 327–333
S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “On the Structure of Symmetry Groups
of Vasil'ev Codes”, Probl. Peredachi Inf., 41:2 (2005), 42–49; Problems Inform. Transmission, 41:2 (2005), 105–112
S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “On the Rank and Kernel Problem for Perfect Codes”, Probl. Peredachi Inf., 39:4 (2003), 30–34; Problems Inform. Transmission, 39:4 (2003), 341–345
S. V. Avgustinovich, F. I. Solov'eva, “To Metric Rigidity of Binary Codes”, Probl. Peredachi Inf., 39:2 (2003), 23–28; Problems Inform. Transmission, 39:2 (2003), 178–183
S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “Perfect codes of complete rank with kernels of large dimensions”, Diskretn. Anal. Issled. Oper., Ser. 1, 8:4 (2001), 3–8
F. I. Solov'eva, S. T. Topalova, “Perfect binary codes and Steiner triple systems with maximum orders of automorphism groups”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000), 101–110
F. I. Solov'eva, S. T. Topalova, “On Automorphism Groups of Perfect Binary Codes and Steiner Triple Systems”, Probl. Peredachi Inf., 36:4 (2000), 53–58; Problems Inform. Transmission, 36:4 (2000), 331–335
S. V. Avgustinovich, F. I. Solov'eva, “On Distance Regularity of Perfect Binary Codes”, Probl. Peredachi Inf., 34:3 (1998), 47–49; Problems Inform. Transmission, 34:3 (1998), 247–249
S. V. Avgustinovich, F. I. Solov'eva, “Construction of Perfect Binary Codes by Sequential Shifts of $\tilde\alpha$-Components”, Probl. Peredachi Inf., 33:3 (1997), 15–21; Problems Inform. Transmission, 33:3 (1997), 202–207
Yu. L. Vasil'ev, F. I. Solov'eva, “Code-Generating Factorizations of the $n$-Dimensional Unit Cube and of Perfect Binary Codes”, Probl. Peredachi Inf., 33:1 (1997), 64–74; Problems Inform. Transmission, 33:1 (1997), 53–61
S. V. Avgustinovich, F. I. Solov'eva, “On the Nonsystematic Perfect Binary Codes”, Probl. Peredachi Inf., 32:3 (1996), 47–50; Problems Inform. Transmission, 32:3 (1996), 258–261
Contact us: