Publications of Qing Xiang

The following papers were accepted or submitted for publication.

  1. (with David Chandler and Peter Sin) The Smith and critical groups of Paley graphs, preprint.
  2. (with Tao Feng and Koji Momihara) Constructions of Strongly Regular Cayley Graphs and Skew Hadamard Difference Sets from Cyclotomic Classes, to appear in Combinatorica.

The following papers were published.

    2014

  1. (with Koji Momihara) Lifting constructions of strongly regular Cayley graphs , Finite Fields Appl. 26 (2014), 86--99.

    2013

  1. (with Tao Feng and Ka Hin Leung) Binary cyclic codes with two primitive nonzeros , Sci. China Math. 56 (2013), 1403-1412.
  2. (with Gennian Ge and Tao Yuan) Constructions of strongly regular Cayley graphs using index four Gauss sums , J. Algebraic Combin. 37 (2013), 313--329.
  3. (with Tao Feng, Bin Wen, and Jianxing Yin) Partial difference sets from quadratic forms and $p$-ary weakly regular bent functions , Number Theory and Related Area, proceedings of a conference in honor of the 70th birthday of Keqin Feng, pp.25--39.

    2012

  1. (with Tao Feng) Strongly regular graphs from unions of cyclotomic classes , J. Combin. Theory (B), 102 (2012), 982--995.
  2. (with Tao Feng) Cyclotomic constructions of skew Hadamard difference sets , J. Combin. Theory (A), 119 (2012), 245--256.
  3. (with David B. Chandler and Junhua Wu) Power sums over subspaces of finite fields , Finite Fields Appl., 18 (2012), 791--799.
  4. Cyclotomy, Gauss sums, difference sets and strongly regular Cayley graphs, p.245--256, Proceedings of Sequences and Their Applications - SETA 2012, 7th International Conference, Waterloo, ON, Canada, June 4-8, 2012.
  5. (with Tao Feng and Fan Wu) Pseudocyclic and non-amorphic fusion schemes of the cyclotomic association schemes , Designs, Codes and Cryptography, 65 (2012), 247--257.

    2011

  1. (with Tao Feng and Zhi-Wei Sun) Exterior algebras and two conjectures on finite abelian groups , Israel J. Math. 182 (2011), 425--437.
  2. (with Peter Sin and Junhua Wu) Dimensions of some binary codes arising from a conic in $PG(2,q)$ , J. Combin. Theory (A), 118 (2011), 853--878.

    2010

  1. (with Jiyou Li and David B. Chandler) Permutation polynomials of degree $6$ or $7$ over finite fields of characteristic $2$, Finite Fields and Their Applications, 16 (2010), 406--419.
  2. (with Willem Haemers) Strongly regular graphs with parameters (4m^4, 2m^4 + m^2, m^4 + m^2, m^4 + m^2) exist for all m>1 , Europ. J. Combin., 31 (2010), 1553--1559.
  3. (with David B. Chandler and Peter Sin) Incidence modules for symplectic spaces in characteristic two , J. Algebra, 323 (2010), 3157--3181.

    2009

  1. (with Tor Helleseth, Henk D. L. Hollmann, Alexander Kholosha and Zeying Wang) Proofs of two conjectures on ternary weakly regular bent functions , IEEE Trans. Inform. Theory, 55 (2009), no. 11, 5272--5283.
  2. (with Cunsheng Ding, Jin Yuan and Pingzhi Yuan) Explicit classes of permutations of F_{3^{3m}}, Science in China Series A: Mathematics, 53 (2009), 639--647.
  3. (with Ka Hin Leung) On the dimensions of the binary codes of a class of unitals , Disc. Math, 309 (2009), 570--575.
  4. Erratum

    2008

  1. (with Tao Feng) Semi-regular relative difference sets with large forbidden subgroups , J. Combin. Theory (A), 115 (2008), 1456--1473.
  2. (with Xiwang Cao and Henk D. L. Hollmann) New Kloosterman sum identities and equalities over finite fields , Finite Fields and Their Appl., 14 (2008), 823--833.

    2007

  1. Modular ranks of some geometric inclusion matrices , Proceedings of the 4th International Congress of Chinese Mathematicians (ICCM 2007), Vol. I, 348--358.
  2. (with Cunsheng Ding and Zeying Wang) Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in $\PG(3,3^{2h+1})$ , J. Combin. Theory (A), 114 (2007), 867--887.
  3. (with Guobiao Weng, Weisheng Qiu, and Zeying Wang) Pseudo-Paley graphs and skew Hadamard difference sets from presemifields , Des. Codes and Cryptogr., 44 (2007), 49--62.
  4. (with David B. Chandler and Peter Sin) The permutation action of finite symplectic groups of odd characteristic on their standard modules , J. Algebra, 318 (2007), 871--892.

    2006

  1. (with David B. Chandler and Peter Sin) The invariant factors of the incidence matrices of points and subspaces in $PG(n,q)$ and $AG(n,q)$, Trans. Amer. Math. Soc., 358 (2006), 4935--4957.
  2. (with Mikhail Muzychuk) Symmetric Bush-type Hadamard matrices of order $4m^4$ exist for all odd $m$, Proceedings of Amer. Math. Soc., 134 (2006), 2197--2204.
  3. (with Henk D. L. Hollmann) Pseudocyclic association schemes arising from the actions of PGL(2,2^m) and P\Gamma L(2,2^m), J. Combin. Theory (A), 113 (2006), 1008--1018.
  4. (with Henk D. L. Hollmann) Association schemes from the action of PGL(2,q) fixing a nonsingular conic in PG(2,q), J. Algebraic Combinatorics 24 (2006), 157--193.
  5. (with James A. Davis) Amorphic association schemes with negative Latin square type graphs, Finite Fields and Their Applications 12 (2006), 595--612.
  6. (with Peter Sin) On the dimensions of certain LDPC codes based on q-regular bipartite graphs, IEEE Trans. Inform. Theory, 52 (2006), 3735--3737.

    2005

  1. Recent results on $p$-ranks and Smith normal forms of some $2-(v,k,\lambda)$ designs, in Coding Theory and Quantum Computing (eds. Evans, et al), proceedings of an international conference on coding theory and quantum computing, May 20--24, 2003, University of Virginia. Contemporary Mathematics 381, 53--67.
  2. Recent progress in algebraic design theory , Finite Fields and Their Aplications (Ten Year Anniversary Edition) 11 (2005), 622--653.
  3. (with Henk D. L. Hollmann) A class of permutation polynomials of $F_{2^m}$ related to Dickson polynomials, Finite Fields and Their Applications 11 (2005), 111--122.

    2004

  1. (with James A. Davis) Negative Latin square type partial difference sets in nonelementary abelian 2-groups , Journal of London Math. Society 70 (2004), 125--141.
  2. (with F. Fiedler and K. H. Leung) On Mathon's construction of maximal arcs in Desarguesian planes. II, J. Combin. Theory (A) 108 (2004), 99-122.
  3. (with Henk D. L. Hollmann) Kloosterman sum identities over F_{2^m} , Disc. Math. 279 (2004), 277--286. Special issue in honor of Zhu Lie.

    2003

  1. (with D. B. Chandler) The invariant factors of some cyclic difference sets , J. Combin. Theory (A) 101 (2003), 131--146.
  2. Association schemes from ovoids in PG(3,q) , J. Geometry 76 (2003), 294--301. (This is basically the talk I gave in "Combinatorics 2002", June 2002, Maratea, Italy.)
  3. (with D. B. Chandler) Cyclic relative difference sets and their p-ranks , Designs, Codes and Cryptography 30 (2003), 325--343.
  4. (with F. Fiedler and K. H. Leung) On Mathon's construction of maximal arcs in Desarguesian planes , Advances in Geometry (2003), special issue dedicated to Adriano Barlotti, S119--S139.

    2002

  1. (with Xiang-dong Hou and Ka Hin Leung) A Generalization of an Addition Theorem of Kneser , J. Number Theory 97 (2002), 1--9.
  2. (with G. L. Ebert, S. Egner, H. D. L. Hollmann) Proof of a Conjecture of De Caen and Van Dam, Europ. J. Combin. 23 (2002), 201--206.
  3. (with K. T. Arasu, Henk D. L. Hollmann, K. Player) On the p-ranks of GMW difference sets, Codes and Designs, Proceedings of a conference honoring Professor Dijen K. Ray-Chaudhuri on the occasion of his 65th birthday, p.9--35, de Gruyter, 2002 .

    2001

  1. (with G. L. Ebert, S. Egner, H. D. L. Hollmann) A Four-Class Association Scheme, J. Combin. Theory (A) 96 (2001), 180--191.
  2. (with Xiang-dong Hou and Ka Hin Leung) New Partial Difference Sets in $Z_{p^2}^t$ and a Related Problem about Galois Rings, Finite Fields and Their Applications 7 (2001), 165--188.
  3. (with Henk D. L. Hollmann) Maximal Arcs in Projective Three-Spaces and Double-Error-Correcting Cyclic Codes, J. Combin. Theory (A) 93 (2001), 168--172.
  4. (with Henk D. L. Hollmann) On Binary Cyclic Codes with Few Weights, in Finite Fields and Applications (editors D. Jungnickel and H. Niederreiter), proceedings of Fq5, Springer (2001), 251--275.
  5. (with Henk D. L. Hollmann) A Proof of the Welch and Niho Conjectures on Crosscorrelations of Binary m-sequences, Finite Fields Appl. 7 (2001), 253--286.
  6. (with Ron D. Baker, Gary L. Ebert, and Ka Hin Leung) A Trace Conjecture and Flag-Transitive Planes, J. Combin. Theory (A) 95 (2001), 158--168.

    2000

  1. (with James A. Davis) Constructions of Low Rank Relative Difference Sets in 2-groups Using Galois Rings, Finite Fields and Their Applications 6 (2000), 130--145.
  2. (with James A. Davis) A Family of Partial Difference Sets with Denniston Parameters in Nonelementary Abelian 2-groups, Europ. J. Combin. 21 (2000), 981--988.

    1999

  1. (with Ron Evans, Henk D. L. Hollmann, Christian Krattenthaler) Gauss sums, Jacobi sums and p-ranks of cyclic difference sets, J. Combin. Theory (A) 87 (1999), 74--119.
  2. (with K. Feng and P. J. Shiue) On Aperiodic and Periodic Complementary Binary Sequences, IEEE Trans. Inform. Theory 45 (1999), 296-303.
  3. (with A. E. Brouwer, R. M. Wilson) Cyclotomy and Strongly Regular Graphs, J. Alg. Combin. 10 (1999), 25--28.
  4. Maximally Nonlinear Functions and Bent Functions, Designs, Codes and Crypt. 17 (1999), 211--218.
  5. Recent Results on Difference Sets with Classical Parameters, in "Difference sets, sequences and their correlation properties", eds. A. Pott, et. al. (1999), 419--437.

    1998

  1. Difference Families from Lines and Half Lines, Europ. J. Combin. 19 (1998), 395-400.
  2. On Reversible Abelian Hadamard Difference Sets, J. Statist. Plann. Inference 73 (1998), 409-416.
  3. On Balanced Binary Sequences with Two-level Autocorrelation Functions, IEEE Trans. Inform. Theory 44 (1998), 3153-3156.

    1997

  1. (with R. M. Wilson) Constructions of Hadamard Difference Sets, J. Combin. Theory Ser. A 77 (1997), no. 1, 148-160. MR 97m:05039.
  2. (with T. Norwood) On GMW Designs and a Conjecture of Assmus and Key, J. Combin. Theory Ser. A 78 (1997) no. 1, 162-168.
  3. (with D. K. Ray-Chaudhuri) New Necessary Conditions for Abelian Hadamard Difference Sets, J. Statist. Plann. Inference 62 (1997) no. 1, 69-79.

    1996

  1. (with Y. Q. Chen, D. K. Ray-Chaudhuri) Constructions of Partial Difference Sets and Relative Difference Sets Using Galois Rings, J. Combin. Theory Ser. A 76 (1996) no. 2, 179-196.
  2. (with Maohua Le)A Result on Ma's Conjecture, J. Combin. Theory Ser. A, 73 (1996), no.1, 181-184. MR 96h:05025.
  3. (with Y. Q. Chen)On Xia's Construction of Hadamard Difference Sets, Finite Fields Appl. 2 (1996), no.1, 87-95. MR 96m:05035.
  4. Note on Paley Type Partial Difference Sets, Groups, difference sets, and the Monster (Columbus, OH, 1993), 239-244, Ohio State Univ. Math. Res. Inst. Publ., 4, de Gruyter, Berlin, 1996. MR 97d:05042.
  5. (with D. K. Ray-Chaudhuri) Constructions of Partial Difference Sets and Relative Difference Sets Using Galois Rings, Des., Codes and Cryptogr.8 (1996), no.1-2, 215-227. MR 97g:05031.

    1995

  1. Reversible (m,n,k,\lambda_1,\lambda_2)-Abelian Divisible Difference Sets with k-\lambda_1 Nonsquare, Discrete Math. 142 (1995), no.1-3, 193-201. MR 96i:05034.
  2. (with Y. Q. Chen) On the Size of the Multiplier Groups of Cyclic Difference Sets, J. Combin. Theory, Ser. A 69 (1995), no. 1, 168-169. MR 95m:05041
  3. (with K. T. Arasu) Multiplier Theorems, J. Combin. Des. 3 (1995), no. 4, 257-268. MR 96b:05032.
  4. A Note on (m,2,m-1,(m-2)/2) Relative Difference Sets, Ars Combin.41 (1995), 199-202. MR 96g:05026.

    1994

  1. (with Y. Q. Chen and S. K. Sehgal) An Exponent Bound on Abelian Skew Hadamard Difference Sets, Des., Codes and Cryptogr. 4 (1994), pp313-317.
  2. Some Results on Multipliers and Numerical Multiplier Groups of Abelian Difference Sets, Graphs and Combinatorics, 10 (1994), no.3, 293-304. MR 96e:05028.

    1992

  1. (with K.T. Arasu) On the Existence of Periodic Complementary Binary Sequences, Des., Codes and Cryptogr. 2 (1992), 257-262. MR 93g:11017.
  2. Some Results on -1 Multiplier of Difference Lists, Combinatroics'90, 559-566, Annals of Discrete Mathematics,52, North-Holland, Amsterdam, 1992. MR 94a:05024.

    1990

  1. (with Wan Di Wei, Shuhong Gao) Extraneous multipliers of abelian difference sets. Combinatorial designs and applications (Huangshan, 1988), 165--173, Lecture Notes in Pure and Appl. Math., 126, Dekker, New York, 1990.