Publications of Qing Xiang
The following papers were accepted or submitted for publication.
- (with David Chandler and Peter Sin) The Smith and critical groups of Paley graphs, preprint.
- (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
- (with Koji Momihara) Lifting constructions of strongly regular Cayley graphs , Finite Fields Appl. 26 (2014), 86--99.
2013
- (with Tao Feng and Ka Hin Leung) Binary cyclic codes with two primitive nonzeros , Sci. China Math. 56 (2013), 1403-1412.
- (with Gennian Ge and Tao Yuan) Constructions of strongly regular Cayley graphs using index four Gauss sums , J. Algebraic Combin. 37 (2013), 313--329.
- (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
- (with Tao Feng) Strongly regular graphs from unions of cyclotomic classes , J. Combin. Theory (B), 102 (2012), 982--995.
- (with Tao Feng) Cyclotomic constructions of skew Hadamard difference sets ,
J. Combin. Theory (A), 119 (2012), 245--256.
- (with David B. Chandler and Junhua Wu) Power sums over subspaces of finite fields , Finite Fields Appl., 18 (2012), 791--799.
- 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.
- (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
- (with Tao Feng and Zhi-Wei Sun) Exterior algebras and two conjectures on finite abelian groups , Israel J. Math. 182 (2011), 425--437.
- (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
- (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.
- (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.
- (with David B. Chandler and Peter Sin) Incidence modules for symplectic spaces in characteristic two , J. Algebra, 323 (2010), 3157--3181.
2009
- (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.
- (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.
- (with Ka Hin Leung) On the dimensions of the binary codes of a class of unitals , Disc. Math, 309 (2009), 570--575.
Erratum
2008
- (with Tao Feng) Semi-regular relative difference sets with large forbidden subgroups , J. Combin. Theory (A), 115 (2008), 1456--1473.
- (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
- Modular ranks of some geometric inclusion matrices , Proceedings of the 4th International Congress of Chinese Mathematicians (ICCM 2007), Vol. I, 348--358.
- (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.
- (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.
- (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
- (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.
- (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.
- (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.
- (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.
- (with James A. Davis) Amorphic association schemes with negative Latin square type graphs, Finite Fields and Their Applications 12 (2006), 595--612.
- (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
- 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.
- Recent progress in algebraic design theory , Finite Fields and Their Aplications (Ten Year Anniversary Edition) 11 (2005), 622--653.
- (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
- (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.
- (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.
- (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
- (with D. B. Chandler) The invariant factors of some cyclic difference sets , J. Combin. Theory (A) 101 (2003), 131--146.
- 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.)
- (with D. B. Chandler) Cyclic relative difference sets and their p-ranks , Designs, Codes and Cryptography 30 (2003), 325--343.
- (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
- (with Xiang-dong Hou and Ka Hin Leung) A Generalization of an Addition Theorem of Kneser , J. Number Theory 97 (2002), 1--9.
- (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.
- (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
- (with G. L. Ebert, S. Egner, H. D. L. Hollmann) A Four-Class Association Scheme, J. Combin. Theory (A) 96 (2001), 180--191.
- (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.
- (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.
- (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.
- (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.
- (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
- (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.
- (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
- (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.
- (with K. Feng and P. J. Shiue) On Aperiodic and Periodic Complementary Binary Sequences, IEEE Trans. Inform. Theory 45 (1999), 296-303.
- (with A. E. Brouwer, R. M. Wilson) Cyclotomy and Strongly Regular Graphs, J. Alg. Combin. 10 (1999), 25--28.
- Maximally Nonlinear Functions and Bent Functions, Designs, Codes and Crypt. 17 (1999), 211--218.
- 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
- Difference Families from Lines and Half Lines, Europ. J. Combin. 19 (1998), 395-400.
- On Reversible Abelian Hadamard Difference Sets, J. Statist. Plann. Inference 73 (1998), 409-416.
- On Balanced Binary Sequences with Two-level Autocorrelation Functions,
IEEE Trans. Inform. Theory 44 (1998), 3153-3156.
1997
- (with R. M. Wilson) Constructions of Hadamard Difference Sets, J. Combin. Theory Ser. A 77 (1997), no. 1, 148-160. MR 97m:05039.
- (with T. Norwood) On GMW Designs and a Conjecture of Assmus and Key,
J. Combin. Theory Ser. A 78 (1997) no. 1, 162-168.
- (with D. K. Ray-Chaudhuri) New Necessary Conditions for Abelian Hadamard
Difference Sets, J. Statist. Plann. Inference 62 (1997) no.
1, 69-79.
1996
- (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.
- (with Maohua Le)A Result on Ma's Conjecture, J. Combin. Theory
Ser. A, 73 (1996), no.1, 181-184. MR 96h:05025.
- (with Y. Q. Chen)On Xia's Construction of Hadamard Difference Sets,
Finite Fields Appl. 2 (1996), no.1, 87-95. MR 96m:05035.
- 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.
- (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
- 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.
- (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
- (with K. T. Arasu) Multiplier Theorems, J. Combin. Des. 3
(1995), no. 4, 257-268. MR 96b:05032.
- A Note on (m,2,m-1,(m-2)/2) Relative Difference Sets, Ars Combin.41 (1995), 199-202. MR 96g:05026.
1994
- (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.
- 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
- (with K.T. Arasu) On the Existence of Periodic Complementary Binary
Sequences, Des., Codes and Cryptogr. 2 (1992), 257-262. MR
93g:11017.
- 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
- (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.