List of Publications by Vladimir D. Tonchev

* Books: [28], [51], [52], [53], [92].
** Handbook chapters: [91], [109].

1975

[1] A simple Boolean function with a complicated realization by the cascade method, Mathematics and Education in Math. (1975) 355-359 (in Bulgarian).

1976

[2] A new class of majority decodable codes, Compt. rend. Acad. bulg. Sci., 29 (1976) 1091-1094.

1977

[3] Self-orthogonal codes and resolvable designs, Compt. rend. Acad. bulg. Sci., 30 (1977) 1235-1237.

1978

[4] On block designs arising from rank 3 graphs, Compt. rend. Acad. bulg. Sci., 31 (1978) 945-948.
[5] Combinatorially self-dual codes, Mathematics and Education in Math. (1978) 515-523. (in Bulgarian).

1979

[6] On the number of equivalence classes of Boolean functions, Compt. rend. Acad. bulg. Sci., 32 (1979) 1609-1610.
[7] Permutation groups and block designs, Mathematics and Education in Math., (1979) 552-564. (in Bulgarian).
[8] Designs with repeated blocks derived from rank 3 graphs, Compt. rend. Acad. bulg. Sci., 32 (1979) 1611-1614.

1980

[9] On the mutual embeddability of (2k,k,k-1) and (2k-1,k,k) designs, J. Combin. Theory, A 29 (1980) 329-335.
[10] On the number of equivalence classes of Boolean functions under a transformation group, IEEE Trans. Inform. Theory, 26 (1980) 625-626 (with J. Denev).
[11] Block designs and 3-designs derived from triangular and lattice graphs, Mathematics and Education in Math., (1980) 95-99 (with D.E. Solakov), (in Bulgarian).

1981

[12] On block designs arising from rank 3 graphs, J. Statist. Plann. Inference, 5 (1981) 399-403.
[13] Rank 3 graphs, block designs and unequal error protection codes, Problemi peredatchi informatsii, 27 (1981), No. 2, 19-25 (in Russian).
[14] A class of unequal error protection codes, Mathematics and Education in Math., (1981) 215-218 (in Bulgarian).
[15] The van der Waerden conjecture is proved, Phys. Math. J. 23 (1981), No. 4, 343-345 (in Bulgarian).
[16] Quasi-residual designs, codes and graphs, Colloq. Math. Soc. Janos Bolyai, 37 (1981) 685-695.

1982

[17] On block designs derived from the lattice graphs, Compt. rend. Acad. bulg. Sci., 35 (1982), 617-619.
[18] Some non-embeddable 2-(11,6,6) designs, Compt. rend. Acad. bulg. Sci., 35 (1982) 621-624 (with D.E. Solakov).
[19] Cyclic 2-(13,5,5) designs, Compt. rend. Acad. bulg. Sci., 35 (1982) 1205-1207 (with R.V. Raev).
[20] Cyclic 2-(17,8,7) designs and related doubly-even codes, Compt. rend. Acad. bulg. Sci., 35 (1982) 1367-1370 (with R.V. Raev).
[21] On some covering by triples, Compt. rend. Acad. bulg. Sci., 35 (1982) 1209-1211 (with D.T. Todorov).
[22] Embeddability of 2-(9,6,10) designs without repeated blocks, Mathematics and Education in Mathematics (1982) 300-306 (in Bulgarian).

1983

[23] Hadamard matrices of order 28 with automorphisms of order 13, J. Combin. Theory, A 35 (1983) 43-57.
[24] Block designs of Hadamard type and self-dual codes, Problemi peredatchi informatsii, 29 (1983), No. 4, 25-30 (in Russian).
[25] On the inequivalence of certain extremal self-dual codes, Compt. rend. Acad. bulg. Sci., 36 (1983) 181-184 (in Russian).
[26] Automorphisms of 2-(33,11,5) designs, Mathematics and Education in Math. (1983) 248-251 (in Bulgarian).
[27] Leonard Euler (1707-1783), Mathematical Education, No. 6, 1983, 21-25 (in Bulgarian).

1984

[28] * ``Combinatorial configurations. Designs, codes, graphs'', Nauka i izkustvo, Sofia 1984 (in Bulgarian; 164 pages).
[29] Non-embeddable quasi-residual designs with large k, J. Combin. Theory, A 37 (1984), 359-362 (with J.H. van Lint).
[30] The isomorphism of the Cohen, Haemers-van Lint and De Clerck- Dye-Thas partial geometries, Discrete Math., 49 (1984) 213-217.
[31] The 3-ranks of the cyclic Steiner 2-(40,4,1) designs, Compt. rend. Acad. bulg. Sci., 37 (1984) 1467-1469.
[32] Latin squares, Mathematical Education, No. 1, 1984, 13-17 (in Bulgarian).

1985

[33] Hadamard matrices of order 28 with automorphisms of order 7, J. Combin. Theory, A 40 (1985), 62-81.
[34] The isomorphism of certain symmetric block designs, Compt. rend. Acad. bulg. Sci., 38 (1985) 161-164.
[35] Combinatorial configurations, codes and automorphisms, Mathematics and Education in Math. (1985) 104-128 (in Bulgarian).

1986

[36] Quasi-symmetric 2-(31,7,7) designs and a revision of Hamada's conjecture, J. Combin. Theory, A 42 (1986), 104-110.
[37] A characterization of designs related to dodecads in the Witt system S(5,8,24), J. Combin. Theory, A 43 (1986) 219-227.
[38] A characterization of designs related to the Witt system S(5,8,24), Math. Z., 191 (1986) 225-230.
[39] Quasi-symmetric designs and self-dual codes, European J. Combin. 7 (1986) 67-73.
[40] Hadamard matrices of order 36 with automorphisms of order 17, Nagoya Math. J., 104 (1986) 163-174.
[41] Embedding of Preece's quasi-residual designs into symmetric designs, Sankhya, B 48 (1986), pt. 2, 216-223.
[42] Two new Steiner systems S(2,4,25), Compt. rend. Acad. bulg. Sci., 39 (1986), No. 5, 47-48.
[43] The symmetric 2-(36,15,6) designs derived from Latin squares of order 6, Compt. rend. Acad. bulg. Sci., 39 (1986), No. 6, 27-29.

1987

[44] Self-dual codes over GF(7), IEEE Trans. Info. Theory, 33 (1987) 723-727 (with Vera Pless).
[45] Embedding of the Witt-Mathieu system S(3,6,22) in a symmetric 2-(78,22,6) design, Geometriae Dedicata 22 (1987) 49-75.
[46] Transitive Steiner triple systems of order 25, Discrete Math. 67 (1987) 211-214.
[47] Steiner triple systems of order 21 with automorphisms of order 7, Ars Combinatoria 23 (1987) 93-96; Erratum: Ars Combinatoria 23 (1995), p. 3.
[48] Symmetric 2-(31,10,3) designs with automorphisms of order 7, Ann. Discr. Math. 34 (1987) 461-464.
[49] Quasi-residual 2-(25,10,6) designs invariant under a dihedral group of order 10, Ann. Discr. Math., 34 (1987) 301-306 (with S. Kapralov and I. Landgev).
[50] On Steiner systems S(2,4,25) invariant under a group of order 9, Ann. Discr. Math., 34 (1987) 307-314 (with E. Kramer and S.S. Magliveras).

1988

[51] * ``Combinatorial configurations'', Longman Scientific and Technical, Wiley, New York 1988. (English translation of [28]; 189 pages)
[52] * ``Combinatorial Configurations'', Visha Shkola, Kiev 1988. (Russian translation of [28]; 155 pages).
[53] * ``Combinatorial Structures and Codes'', Kliment Ohridski University Press, Sofia 1988 (in Bulgarian; 175 pages).
[54] Symmetric designs without ovals and extremal self-dual codes, Ann. Discr. Math., 37 (1988) 451-458.
[55] On the covering radius of binary (14,6) codes containing the all-one vector, IEEE Trans. Info. Theory, 34 (1988) 591-593 (with S. Dodunekov and K. Manev).
[56] The automorphism groups of the known 2-(91,6,1) designs, Compt. rend. Acad. bulg. Sci., 41 (4) (1988) 15-16 (with S. Stoichev).

1989

[57] Self-orthogonal designs and extremal doubly-even codes, J. Combin. Theory, A 52 (1989), 197-205.
[58] New extremal doubly-even codes of length 56 derived from Hadamard matrices of order 28, Discr. Math. 76 (1989) 45-49 (with F.C. Bussemaker).
[59] Automorphisms of 2-(22,8,4) designs, Discr. Math. 77 (1989) 177-189 (with I. Landgev).
[60] Results on the support of BIB designs, J. Statist. Plann. Inference 22 (1989) 295-306 (with S. Hedayat and I. Landgev).

1990

[61] A new design, in: "Coding Theory and Design Theory. Part II. Design Theory", D. Ray-Chaudhuri ed., The IMA Volumes in Mathematics and its Applications, Vol. 21, Springer-Verlag, New York 1990, pp.251-256. (with J.H. van Lint and I. Landgev).
[62] Extremal doubly-even codes of length 40 derived from Hadamard matrices of order 20, Discr. Math. 82 (1990), 317-321 (with F.C. Bussemaker).
[63] Extremal doubly-even codes of length 64 derived from symmetric designs, Discr. Math. 83(1990), 285-289 (with S. Kapralov).
[64] Self-orthogonal designs, Contemporary Math., 111 (1990),219-235.
[65] Some new classes of codes admitting majority decoding, Mathematics and Mathematical Education, 1990, 334-337 (in Bulgarian).

1991

[66] Unitals in the Holz design on 28 points, Geom. Dedicata 38 (1991), 357-363.
[67] Intersection numbers of quasi-multiples of symmetric designs, in: "Advances in Finite Geometries and Designs", J.W.P. Hirschfeld, D.R. Hughes and J.A. Thas eds., Oxford University Press, 1991, 227-236.(with D. Jungnickel).
[68] Exponential number of quasi-symmetric SDP designs and codes meeting the Grey-Rankin bound, Designs, Codes and Cryptography, 1 (1991), 247-253 (with D. Jungnickel).
[69] Self-dual codes and Hadamard matrices, Discr. Appl. Math. 33 (1991), 235-240.
[70] Cyclic 2-(91,6,1) designs with multiplier automorphisms, Discrete Math. 97 (1991) 265-268. (with Zvonimir Janko).
[71] Problems 150-151, Discrete Math. 97 (1991), 422-423.

1992

[72] On symmetric and quasi-symmetric designs with the symmetric difference property and their codes, J. Combin. Theory A 59 (1992), 40-50 (with D. Jungnickel).
[73] Some small non-embeddable designs, Discrete Math. 106/107 (1992), 489-492.
[74] On Kirkman triple systems of order 33, Discrete Math. 106/107 (1992), 493-496 (with S.A. Vanstone).
[75] Concerning multiplier automorphisms of cyclic Steiner triple systems, Designs, Codes and Cryptography 2 (1992), 237-251 (with C.J. Colbourn, E. Mendelsohn and C.E. Praeger).
[76] Extremal self-dual codes from symmetric designs, Discrete Math. 110 (1992), 265-268 (with E. Spence).
[77] Partial geometries and quadrics, Sankhy ser. A 54 (1992), 137-145 (with Frank De Clerck).

1993

[78] On the existence of a certain (64,32,12) extremal code, IEEE Transactions on Information Theory 39 (1993), 214-215 (with Vera Pless and Jef Leon).
[79] A class of non-embeddable designs, J. Combin. Theory , Ser. A 62 (1993), 252-260 (with J.H. van Lint)
[80] A design and a code invariant under the simple group Co3, J. Combin. Theory, Ser. A 62 (1993), 225-233 (with W. Haemers, C. Parker and Vera Pless).
[81] A symmetric 2-(160,54,18) design, J. Combin. Designs 1 (1993), 65-68 (with E. Spence and Tran van Trung).
[82] On the extendability of Steiner t-designs, J. Combin. Designs 1 (1993), 239-247. (with A. Baartmans and Ian Blake).
[83] Symmetric (31,10,3) designs with trivial automorphism group, Ars Combinatoria 36 (1993), 249-254.
[84] Quasi-symmetric designs, codes, quadrics, and hyperplane sections, Geometriae Dedicata 48 (1993), 295-308.

1994

[85] The Preparata codes and a class of 4-designs, J. Combinatorial Designs 2 (1994), 167-170. (with Alphonse Baartmans and Iliya Bluskov)
[86] Designs with the symmetric difference property on 64 points and their groups, J. Combin. Theory, Ser. A 67 (1994), 23-43. (with C. Parker and E. Spence).

1995

[87] On quasi-symmetric 2-(28,12,11) and 2-(36,16,12) designs, Designs, Codes and Cryptography) 5 (1995), 43-56 (with C. Lam and L. Thiel).
[88] The existence of extremal [50,25,10] codes and quasi-symmetric 2-(49,9,6) designs, Designs, Codes, and Cryptography (with W. Cary Huffman), 6 (1995), 97-106.
[89] Singly-even self-dual codes and Hadamard matrices, Lecture Notes in Computer Science 948 (1995), pp. 279-284. ISBN 3-540-60114-7 (with M. Harada)
[90] Linear codes and doubly-transitive symmetric designs, Linear Algebra and its Applications 226-228 (1995), 237-246. (with C. Parker)

1996

[91] ** ``Codes'', a Chapter in: ``The CRC Handbook of Combinatorial Designs'', C.J. Colbourn and J.H. Dinitz eds., CRC Press, New York 1996, pp. 517-543.
[92] * ``Codes, Designs, and Geometry'', Proceedings of the Second Upper Michigan Combinatorics Workshop, Kluwer, Boston 1996, edited by Vladimir Tonchev.
[93] The uniformly packed binary [28,21,3] and [35,29,3] codes, Discrete Math. 149 (1996), 283-288.
[94] A class of Steiner 4-wise balanced designs derived from Preparata codes, J. Combin. Designs 4 (1996), 203-204. [ Click here to load PS format]
[95] On the binary codes of Steiner triple systems, Designs, Codes and Cryptography 8 (1996), 29-43 (with A. Baartmans and I. Landjev)
[96] Spreads in strongly regular graphs, Designs, Codes and Cryptography, 8 (1996), 145-157 (with W. Haemers)
[97] The existence of certain extremal [54,27,10] self-dual codes, IEEE Trans. Inform. Theory 42 (1996), 1628-1631 (with V.Y. Yorgov)
[98] Classification of affine resolvable 2-(27,9,4) designs, J. Statistical Planning and Inference 56 Issue 2, (1996), 187-202. (with Clement Lam). [ PDF file]

1997

[99] Codes of Steiner triple systems of order 15, J. Stat. Plan. Inf. 58 (1997), 207-216 (with Robert Weishaar).
[100] Binary codes derived from the Hoffman-Singleton and Higman-Sims graphs, IEEE Trans. Info. Theory 43 (1997), 1021-1025. [ PDF file]
[101] Linear codes and the existence of a reversible Hadamard difference set in Z2xZ2xZ5^4, Journal of Combin. Theory, A 79 (1997), 161-167 (with M. van Eupen).
[102] Computational results for the known biplanes of order 9, in: ``Geometry, Combinatorial Designs and Related Structures'', J.W.P Hirschfeld, S.S. Magliveras, and M.J. de Resmini eds., London Math. Soc. Lecture Note Ser. vol. 245 (1997), pp.113-122 (with Jenny Key).
[103] Embedding Partial Geometries in Steiner Designs, in: ``Geometry, Combinatorial Designs and Related Structures'', J.W.P Hirschfeld, S.S. Magliveras, and M.J. de Resmini eds., London Math. Soc. Lecture Note Ser. vol. 245 (1997), pp.33-41 (with A. Brouwer and W. Haemers).

1998

[104] Characterizing the Hermitian and Ree unitals on 28 points, Designs, Codes and Cryptography 13 (1998), 57-61 (with G. McGuire and H. N. Ward).
[105] Maximum disjoint bases and constant weight codes, IEEE Trans. Info. Theory 44 (1998), 333-334.
[106] Quasi-symmetric 2-(28,12,11) Designs with an Automorphism of Order 7, J. Combin. Designs 6 (1998), 213-223 (with Yuan Ding, Sheridan Houghten, Clement Lam, Suzan Smith and Larry Thiel)
[107] Computing linear codes and unitals, Designs, Codes and Cryptography 14 (1998), 39-52 (with David Jaffe)
[108] New designs with block size 7, J. Combin. Theory A 83 (1998), 152-157 (with Z. Janko).
[109] ** ``Codes and Designs'', in: ``Handbook of Coding Theory'', V.S. Pless and W.C. Huffman eds., Chapter 15, pp. 1229-1267, Elsevier Science B.V., 1998.

1999


[110] Decompositions of difference sets, J. Algebra 217 (1999), 21-39. (with D. Jungnickel)
[111] Perfect Codes and Balanced Generalized Weighing Matrices, Finite Fields and their Appl. 5 (1999), 294-300. (with D. Jungnickel). [ Click here for PDF file]
[112] Linear perfect codes and a characterization of the classical designs, Designs, Codes and Cryptography. 17 (1999), 121-128. [ PDF file]

2000


[113] Maximal arcs and disjoint maximal arcs in projective planes of order 16, J. Geometry 67 (2000), 117-126. (with N. Hamilton and S. Stoichev)
[114] Corrigendum to ``Classification of affine resolvable 2-(27,9,4) designs: Corrigendum'', J. Statistical Planning and Inference 86 (2000) 277-278. (with Clement Lam) [ PDF file]
[115] On symmetric nets and generalized Hadamard matrices from affine designs J. of Geometry 67 (2000), 180-187. (with V. Mavron)
[116] Unital designs in planes of order 16, Discrete Appl. Math. 102 (2000), 151-158. (with S. Stoichev)
[117] Bounds on the number of Affine, Symmetric and Hadamard Designs and Matrices J. Combin. Theory A 92 (2000), 186-196 (with C. Lam and S. Lam).

2001


[118] Bush-type Hadamard matrices and symmetric designs, J. Combin. Designs 9 (2001), 72-78. (with Z. Janko and H. Kharaghani)
[119] The [52,26,10] binary self-dual codes with an automorphism of order 7, Finite Fields and their Applications 7 (2001), 241-349. (with Cary W. Huffman).
[120] Special Issue on Designs Combinatorics: In honor of S. S. Shrikhande, J. of Statistical Planning and Inference, Volume 95, No. 1-2 (2001), 360 pages, Edited by V.D. Tonchev, S. Hedayat, N. Singhi and K.D. Vijayan.
[121] Bounds on the number of Hadamard designs of even order, J. Combinatorial Designs 9 (2001) 363-378. (with C. Lam and S. Lam)
[122] A mass formula for Steiner triple systems STS(2^n-1) of 2-rank 2^n-n., J. Combin. Theory, Ser. A 95 (2001), 197-208.
[123] The existence of a Bush--type Hadamard matrix of order 324 and two new infinite classes of symmetric designs, Designs, Codes and Cryptography 24 (2001), 225-232. (with Z. Janko and H. Kharaghani)

2002


[124] Vladimir D. Tonchev, A Varshamov-Gilbert bound for a class of formally self-dual codes and related quantum codes, IEEE Trans. Information Theory. 48 (2002), 975-977.
[125] V.D. Tonchev, Error-correcting codes from graphs, Discrete Math. 257 (2002), 549-557.
[126] Perfect Codes and Balanced Generalized Weighing Matrices, II, Finite Fields and their Appl. 8 (2002), 155-165 (with Dieter Jungnickel).
[127] On a class of twin balanced incomplete block designs, in: ``Codes and Designs'', K.T. Arasu and A. Seress eds., de Gruyter, New York 2002, pp. 157-164 (with Hadi Kharaghani).
[128] A new bound on the number of designs with classical affine parameters, Designs, Codes and Cryptography 27 (2002), 111-117 (with Clement Lam).
[129] V. I. Levenshtein and V.D. Tonchev, Constructions of difference systems of sets, in: ``Algebraic and and Combinatorial Coding Theory'', Eight International Workshop Proc., St. Petersburg, Russia, Sept. 2002, pp. 194-197.

2003


[130] M. Harada and V.D. Tonchev, Self-Orthogonal Codes from Symmetric Designs with Fixed-Point-Free Automorphisms, Discrete Math. 264 (2003), 81-90.
[131] V.D. Tonchev, A formula for the number of Steiner quadruple systems on 2^n points of 2-rank 2^n-n, J. Combinatorial Designs , 11 (2003), 260-274.
[132] A. Betten, D. Betten and V.D. Tonchev, Unitals and Codes, Discrete Math. 267 (2003), 23-33.
[133] V. D. Tonchev, A note on MDS Codes, n-Arcs and Complete Designs, Designs, Codes and Cryptography 29 (2003), 247-250.
[134] V. D. Tonchev, Difference systems of sets and code synchronization, Rendiconti del Seminario Matematico di Messina , Series II, vol. 9 (2003), 217-226.

2004


[135] A new quasi-symmetric 2-(56,16,6) design obtained from codes, Discrete Math 29 (2004), 231-234 (with A. Munemasa).
[136] V.D. Tonchev, On generalized Hadamard matrices of minimum rank, Finite Fields and their Appl. 10 (2004), 522-529.

2005


[137] C. Lam, M. Harada and V.D. Tonchev, Symmetric (4,4)-nets and generalized Hadamard matrices over groups of order 4, Designs, Codes and Cryptography , 34 (2005), 71-87.
[136] V.D. Tonchev, Affine designs and linear orthogonal arrays, Discrete Math. 294 (2005), 219-222.
[137] M. Harada, A. Munemasa and V.D. Tonchev, A Characterization of Designs Related to an Extremal Doubly-Even Self-Dual Code of Length 48, Annals of Combinatorics f 9 (2005), 189-198.


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