Qiang (Steven) Wang's publications

Books

  • Functional graphs of generalized cyclotomic mappings of finite fields by A. Bors, D. Panario and Q. Wang, Memoirs of the European Mathematical Society, vol. 23, 2026, 270pp.

    Papers

    1. Construction of (n,n) -functions with low differential-linear uniformity (with X. Xie, N. Li, X. Zeng, Y. Du), Finite Fields Appl. 109 (2026), Paper No. 102710, 20 pp.

    2. An effective approach to enumerate universal cycles for k -permutations(with Z. Chang, J. Xue), Cryptogr. Commun. 17 (2025), no. 4, 977–988.

    3. Efficient generation of odd order de Bruijn sequence with the same complement and reverse sequences (with Z. Chang), Des. Codes Cryptogr. 93 (2025), no. 6, 1935–1949.

    4. Linear codes with few weights from vectorial dual-bent functions (with Z. Wang, S. Yang), Finite Fields Appl. 108 (2025), Paper No. 102660, 29 pp.

    5. A survey of compositional inverses of permutation polynomials over finite fields. Designs, Codes and Cryptography 93 (2025), 831–870. online first.

    6. Counting polynomials with distinct roots using subset sum (with S. Kuttner and Z. Gao), Lecture Notes in Comput. Sci. 15176 Springer, Cham, 2025, 154-170.

    7. On constructing bent functions from cyclotomic mappings (with X. Xie, N. Li, X. Zeng), IEEE Trans. Inform. Theory 71 (2025), no. 2, 1389–1399.

    8. The complexity of elliptic normal bases (with D. Panario, M. Sall), Finite Fields Appl. 103 (2025), Paper No. 102570, 16 pp.

    9. On the stability of $b^q(x+a)^{q+1}+x$ from the perspective of periodic sequences (with T. Lin), Cryptogr. Commun. 16 (2024), no. 6, 1327–1346.

    10. Towards a classification of permutation binomials of the form $x^i + ax$ over $\mathbb{F}_{2^n}$ (with Y. Li and X. Feng). Designs, Codes and Cryptography, 92 (2024), 3859–3875. online first.

    11. Additive codes with few weights (with D. Panario, M. Sahin). Cryptography and Communications 16 (2024), no. 5, 1077-1102.

    12. On stable polynomials of degrees 2, 3, 4. (with T. Lin). Finite Fields Appl. Volume 99, 2024, 102474, 15pp.

    13. Constructing permuation polynomials from permutation polynomials of subfields (with L. Reis). Finite Fields Appl. Volume 96, 2024, 102415, 19pp.

    14. Some classes of permuation binomials and trinomials of index $q-1$ over $\mathbb{F}_{q^n}$ (with R. Gupta, L. Quoos), Cryptography and Communications 16 (2024), no. 2, 387-402.

    15. Generalized Lucas polynomials over finite fields (with L. Li, X. Zeng). Finite Fields Appl. Volume 89, 2023, 102207, 27pp.

    16. Compositions and parities of complete mappings and of orthomorphisms, (with A. Bors). Journal of Combinatorial Theory Series A Volume 196, May 2023, 105723, 53pp.

    17. Two-weight or three-weight binary linear codes from cyclotomic mappings (with J. Fang, Y. Sun, Y. Wang). Finite Fields Appl. 85 (2023), Paper No. 102114, 19 pp.

    18. Coset-wise affine functions and cycle types of complete mappings (with A. Bors). Finite Fields Appl. 83 (2022), Paper No. 102088, 32 pp.

    19. Further improvement on index bounds (with Y Wu and Y. Lee). Des. Codes Cryptogr. 90 (2022), no. 12, 2813–2821.

    20. On the enumeration of polynomials with prescribed factorization pattern (with S. Kuttner). Finite Fields Appl. 81 (2022), Paper No. 102023.

    21. Counting irreducible polynomials with prescribed coefficients over a finite field (with Z. Gao, S. Kuttner). Finite Fields Appl. 80 (2022), Paper No. 102023.

    22. Generalized cyclotomic mappings: switching between polynomial, cyclotomic, and wreath product form (with A. Bors). Commun. Math. Res. 38 (2022), no. 2, 246-318, 73pp.

    23. The additive index of polynomials over finite fields (with L. Reis). Finite Fields Appl. 79 (2022), Paper No. 102002, 16 pp.

    24. Cycle types of complete mappings of finite fields (with A. Bors). Journal of Algebra 591 (2022), 577-610.

    25. On the stability of periodic binary sequences with zone restriction (with M. Su), Applicable Algebra in Engineering, Communication and Computing 33 (2022), 485–504. https://doi.org/10.1007/s00200-020-00467-3

    26. A framework of constructing placement delivery arrays for centralized coded caching (with M. Chen, J. Jiang, X. Zhong). IEEE Trans. Inform. Theory 67 (2021), no. 11, 7121-7131.

    27. Finding compositional inverses of permutations from the AGW criterion (with T. Niu, K. Li, L. Qu). IEEE Trans. Inform. Theory 67 (2021), no. 8, 4975-4985.

    28. A family of Hermitian dual-containing constacyclic codes and related quantum codes (with X. Zhao, X. Li, T. Yan). Quantum Inf. Process. 20 (2021), no. 5, Paper No. 186, 22 pp.

    29. Exponential Sums with Sparse Polynomials over Finite Fields (with I. E. Shparlinski). SIAM Journal on Discrete Mathematics 35 (2021), no. 2, 976-987.

    30. An efficiently generated family of binary de Bruijn sequences (with Y. Zhu, Z. Chang, M. F. Ezerman). Discrete Mathematics 344 (2021), no. 6, 112368, 11 pp.

    31. Several classes of complete permutation polynomials with Niho exponents (with L. Li, Y. Xu, X. Zeng). Finite Fields and Their Applications 72 (2021), 101831, 31 pp.

    32. On enumeration of irreducible polynomials and related objects over a finite field with respect to their trace and the norm. Finite Fields and Their Applications 69 (2021), 101770, 25pp.

    33. Boomerang uniformity of normalized permutation polynomials of low degree (with Y. Wang, W. Zhang), Finite Fields and Their Applications 64 (2020), 101664.

    34. Cycle strutures of a class of Cascaded FSRs (with Z. Chang and G. Gong), IEEE Transactions on Information Theory 66 (2020), no. 6, 3766-3774.

    35. Construction of irreducible polynomials through rational transformations (with D. Panario and L. Reis), Journal of Pure and Applied Algebra 224 (2020), no. 5, 106241.

    36. On Inverses of Permutation Polynomials of Small Degree over Finite Fields (with Y. Zheng and W. Wei), IEEE Transactions on Information Theory, 66 (2020), no. 2, 914–922.

    37. New constructions of involutions over finite fields (with T. Niu, K. Li, L. Qu), Cryptography and Communications 12 (2020), no. 2, 165-185.

    38. Fixed points of rational functions satisfying the Carlitz property (with K. Chubb, D. Panario). Appl. Algebra Engrg. Comm. Comput. 30 (2019), no. 5, 417-439.

    39. On the Derivative Imbalance and Ambiguity of Functions (with C. Carlet, S. Fu, X. Feng), IEEE Transactions on Information Theory 65 (2019), no. 9, 5833- 5845.

    40. Polynomials over finite fields: an index approach, Combinatorics and Finite Fields. Difference Sets, Polynomials, Pseudorandomness and Applications , Degruyter, 2019, page 319-348. Preprint

    41. A Generalized Grouping Scheme in Coded Caching (with M. Cheng, J. Jiang, Y. Yao), IEEE Transactions on Communications , 67 (2019), 3422 - 3430.

    42. Further results on complete permutation monomials over finite fields (with X. Feng, D. Lin, L. Wang), Finite Fields and Their Applications , 57 (2019), 47-59.

    43. Improved Bounds on $2$-Frameproof Codes with Length $4$ (with M. Chen, J. Jiang), Designs Codes and Cryptography 87 (2019), no. 1, 97-106.

    44. A Recursive Construction of Permutation Polynomials over $\mathbb{F}_{q^2}$ with Odd Characteristic Related to R\'{e}dei Functions (with S. Fu, X. Feng, D. Lin), Designs Codes and Cryptography, 87 (2019), no. 7, 1481-1498.

    45. A lower bound on the 2-adic complexity of modified Jacobi sequence (with Y. Sun, T. Yan), Cryptography and Communications, 11 (2019), no. 2, 337-349.

    46. Counting compositions over finite abelian groups (with Z. Gao and A. McFie), Electronic Journal of Combinatoric , (2018), no. 2, Paper 2.19, 23 pp.

    47. Compositional Inverses of Permutation Polynomials of the Form $x^rh\left(x^s\right)$ over Finite Fields (with K. Li and L. Qu), Cryptography and Communications 11 (2019), no. 2, 279–298.

    48. New Constructions of Permutation Polynomials of the Form $x^rh\left(x^{q-1}\right)$ over $\mathbb{F}_{q^2}$ (with K. Li and L. Qu), Designs Codes and Cryptography, 86 (2018), no. 10, 2379–2405.

    49. Nonlinear vectorial primitive recursive sequences (with S. U. Hasan and D. Panario), Cryptography and Communications. 10.1007/s12095-017-0265-2.

    50. A new proof of the Hansen-Mullen irreducibility conjecture (with Tuxanidy), Canadian Journal of Mathematics , 70 (2018), no. 6, 1373–1389. http://dx.doi.org/10.4153/CJM-2017-022-1

    51. Non-homogeneous conditional recurrences (with D. Panario and M. Sahin), to appear in Linear and Multilinear Algebra.

    52. Characteristic digit-sum sequences (with Tuxanidy), Cryptography and Communications 10 (2018), no. 4, 705-717.

    53. Ambiguity, deficiency and differential spectrum of normalized permutation polynomials over finite fields (with D. Panario, D. Santana), Finite Fields and their Applications 47 (2017), 330-350.

    54. The exact autocorrelation distribution and $2$-adic complexity of a class of binary sequences with almost optimal autocorrelation (with Y. Sun, T. Yan), Cryptography and Communications 10 (2018), no. 3, 467-477.

    55. A note on inverses of cyclotomic mapping permutation polynomials over finite fields, Finite Fields Appl. 45 (2017), 422-427.

    56. The T4 and G4 constructions of Costas arrays (with T. Trudgian). J. Combin. Math. Combin. Comput. 100 (2017), 217–221.

    57. Compositional inverses and complete mappings over finite fields (with A. Tuxanidy), Discrete Appl. Math. 217 (2017), part 2, 318–329.

    58. On coefficients of powers of polynomials and their compositions over finite fields (with G. L. Mullen, A. Muratovic-Ribic). Contemporary developments in finite fields and applications , 270–281, World Sci. Publ., Hackensack, NJ, 2016.

    59. Index bounds for character sums of polynomials over finite fields (with D. Wan), Designs Codes and Cryptography 81 (2016), no. 3, 459–468.

    60. On the number of $N$-free elements with prescribed trace (with A. Tuxanidy), Journal of Number Theory 160 (2016), 536–565.

    61. Formulas for p-th root computations in finite fields of characteristic p (with L. Perin, R. Custodio and D. Panario), Electronics Letters 52, 117-119, 2016.

    62. An asymptotic formula for the number of irreducible transformation shift registers (with S. D. Cohen, S. U. Hasan, D. Panario). Linear Algebra Appl. 484 (2015), 46-62

    63. Linear complexity profile and correlation measure of interleaved sequences (with J. He, D. Panario and A. Winterhof), Cryptography and Communications 7 (2015), no. 4, 497–508.

    64. A probabilistic approach to value sets of polynomials over finite fields (with Z. Gao), Finite Fields Appl. 33 (2015), 160-174

    65. Index bounds for value sets of polynomials over finite fields (with G. L. Mullen, D. Wan), Applied Algebra and Number Theory , Cambridge University Press, 2014, pages 280-296. or Preprint

    66. The multisubset problem for finite abelian groups (with A. Muratovic-Ribic), Ars Mathematica Contemporanea 8 (2015), no. 2, 417–423. arXiv 1305.3259 or Preprint

    67. On the characterization of a semi-multiplicative analogue of planar functions over finite fields (with A. Muratovic-Ribic, A. Pott, D. Thomson), Topics in finite fields , 317–325, Contemp. Math., 632, Amer. Math. Soc., Providence, RI, 2015.

    68. General conditional recurrences (with D. Panario, M. Sahin, Murat and W. Webb). Appl. Math. Comput. 243 (2014), 220–231.

    69. Roots and coefficients of polynomials over finite fields (with S. Kopparty) Finite Fields Appl. 29 (2014), 198–201.

    70. On the inverses of some classes of permutations of finite field (with A. Tuxanidy), Finite Fields Appl. 28 (2014), 244-281.

    71. Cyclotomy and permutation polynomials of large indices, IEEE Transactions on Information Theory 59 (2013), 5616-5626.

    72. Permutation polynomials of one variable (with G. L. Mullen), Section 8.1, In Handbook of Finite Fields , Chapman and Hall/CRC, 2013, page 215-230. Preprint

    73. Dickson polynomials (with J. L. Yucas), Section 9.6, In Handbook of Finite Fields , Chapman and Hall/CRC, 2013, page 282-290. Preprint

    74. A family of Fibonacci-like conditional sequences (with M. Sahin and D. Panario), INTEGERS Electronic Journal of Combinatorial Number Theory , 13, A78, 2013, 14pp.

    75. Symmetries of codeword stabilized quantum codes (with Salman Beigi, Jianxin Chen, Markus Grassl, Zhengfeng Ji and Bei Zeng), LIPIcs. Leibniz Int. Proc. Inform., 22 Schloss Dagstuhl. Leibniz-Zentrum für Informatik, Wadern, 2013, 192–206.

    76. Ambiguity and deficiency of permutations over finite fields with linearized difference map (with D. Panario, A. Sakzad, B. Stevens, D. Thomson), IEEE Transactions on Information Theory 59, 5616-5626, 2013.

    77. Partitions and Compositions over Finite Fields (with A. Muratovic-Ribic), The Electronic Journal of Combinatorics Volume 20, Issue 1 (2013). Online publication

    78. Generalized Alcuin's Sequence (with D. Panario, M. Sahin), The Electronic Journal of Combinatorics , Volume 19, Issue 4 , P55 (2012). Online publication

    79. Value sets of polynomial maps over finite fields (with G. L. Mullen and D. Wan), Quarterly J. Mathematics , Oxford, 64 (2013), no. 4, 1191-1196. Online publication

    80. Composed products and factors of cyclotomic polynomials over finite fields (with A. Tuxanidy), Designs, Codes and Cryptography. (A. Tuxanidy was my Honours project student). Preprint

    81. Dickson polynomials over finite fields (with J. Yucas), Finite Fields and their Applications 18 (2012), no. 4, 814–831. Preprint

    82. On a conjecture of polynomials over finite fields of precribed range (with A. Muratovic-Ribic), Finite Fields Appl. 18 (2012), no. 4, 728–737. Preprint

    83. Word-Oriented Transformation Shift Registers and Their Linear Complexity (with S. U. Hasan, D. Panario), Proceeding of SETA 2012: SEquences and Their Applications, University of Waterloo, June 4-8, 2012, Lecture Notes in Computer Science 7280, Springer, 190-202, 2012.

    84. Ambiguity and Deficiency of permutations (with D. Panario, A. Sakzad, B. Stevens), ITW 2011 (IEEE Information Theory Workshop) , IEEE Xplore, 165-169, 2011.

    85. Divisibility of polynomials over finite fields and combinatorial applications (with D. Panario, O. Sosnovski, B. Stevens), Designs, Codes and Cryptography 63 (2012), Number 3, 425-445. (O. Sosnovski was my Honours project student) Preprint

    86. On explicit factors of cyclotomic polynomials over finite fields (with L. Wang), Designs, Codes and Cryptography 63 (2012), Number 1, Pages 87-104. Preprint

    87. Two new measures for permutations: ambiguity and deficiency (with D. Panario, A. Sakzad, B. Stevens), IEEE Transactions on Information Theory 57 (2011), no. 11, 1-10. Preprint

    88. On coefficients of polynomials over finite fields (with A. Muratović-Ribić ), Finite Fields Appl. 17 (2011), no. 6, 575-599. Preprint

    89. On constructing permutations of finite fields (with A. Akbary, D. Ghioca), Finite Fields Appl. 17 (2011), 51-67. Preprint

    90. On generalized Lucas sequences, Combinatorics and Graphs: the twentieth anniversary conference of IPM, May 15-21, 2009, Contemporary Methematics 531 (2010), 127-141. Preprint

    91. A Karatsuba's algorithm for polynomial multiplication in Chebyshev form (with J. Bandeira Lima and D. Panario), IEEE Transactions on Computers 59 (2010), 835-841. Preprint

    92. The number of irreducible polynomials of degree n over F_q with given trace and constant terms (with B. Omidi Koma and D. Panario), Discrete Mathematics, 310 (2010), 1282-1292. Preprint

    93. Ambiguity and deficiency in Costas arrays and APN permutations (with D. Panario and B. Stevens), LATIN 2010 (Latin American Theoretical INformatics) , Lecture Notes in Computer Science 6034, Springer, 397-406, 2010.

    94. A family of binary sequences from interleaved construction and their cryptographic properties (with J. J. He, D. Panario), Finite Fields: Theory and Applications , Contemporary Mathamtics, 518 (2010), 209-224. Preprint

    95. Results on permutations with distinct difference property (with J. Bell), Contributions to Discrete Mathematics Vol 4, No 1 (2009). (J. Bell was my NSERC summer research student).

    96. On the inverse permutation polynomials, Finite Fields Appl. 15 (2009), no. 2, 207--213. Preprint

    97. On Permutation polynomials with prescribed shape (with A. Akbary, D. Ghioca), Finite Fields Appl. 15 (2009), no. 2, 195--206. Preprint

    98. An answer to Hirasaka and Muzychuk: every $p$-Schur ring over $C_p^3$ is Schurian (with P. Spiga), Discrete Mathematics 308 (2008), no. 9, 1760-1763. Preprint

    99. Cyclotomic mapping permutation polynomials over finite fields, Sequences, subsequences, and Consequences (International Workshop, SSC 2007, Los Angeles, CA, USA, May 31 - June 2, 2007), LNCS 4893, 119-128. (note: (r, (q-1)/d) =1 was missing in the sum of Corollary 1 in the original publication) Preprint

    100. On polynomials of the form $x^rf(x^{(q-1)/l})$ (with A. Akbary), International Journal of Mathematics and Mathematical Sciences, Volume 2007 (2007), Article ID 23408, 7 pages. Open Access

    101. Division of trinomials by pentanomials and orthogonal arrays (with M. Dewar, L. Moura, D. Panario, B. Stevens), Designs, Codes and Cryptography , 45 (2007), no. 1, 1-17.

    102. On some classes of permutation polynomials" (with A. Akbary, S. Alaric), International Journal of Number Theory , Vol 4, No. 1 (2008), 121 - 133. Preprint

    103. Null Extensions and Generalized Inflations of Brandt Semigroups" (with S. L. Wismath), Semigroup Forum , 74 (2007), no. 2, 274--292.

    104. Generalized Inflations of Completely Simple Semigroups" (with S. L. Wismath), Algebra Colloquium 14 (2007), no. 1, 103-116.

    105. The Inflation Class Operator" (with A. Christie, S. L. Wismath), Algebra Universalis 56 (2007), 107 - 118.

    106. A generalized Lucas sequence and permutation binomials" (with A. Akbary), Proceedings of the American Mathematical Society 134 (2006), no 1, 15-22. Preprint

    107. The number of permutation binomials over $\mathbb{F}_{4p+1}$ where $p$ and $4p+1$ are primes" (with A. Masuda, D. Panario), Electron. J. Combin. 13 (2006), R65.

    108. A note on hereditary semigroup algebras" (with X. Q. Chen), Pragmatic algebra, 181--186, SAS Int. Publ., Delhi, 2006

    109. On some permutation polynomials over finite fields" (with A. Akbary), International Journal of Mathematics and Mathematical Sciences (IJMMS) 16 (2005), 2631-2640. Preprint

    110. Minimal Characteristic Algebras for k-Normality" (with A. Christie and S. L. Wismath), Scientiae Mathematicae Japonicae (SCMJ) 61. No.3 (2005), 547-565.

    111. Generalized Inflations and Null Extensions" (with S. L. Wismath), Discussiones Mathematicae General Algebra and Applications 24 (2004), no. 2, 225-249.

    112. Height one prime ideals in semigroup algebras satisfying a polynomial identity" (with E. Jespers), Journal of Algebra 248 (2002), no. 1, 118-131.

    113. Noetherian unique factorization semigroup algebras" (with E. Jespers), Communications in Algebra 29 (2001), no. 12, 5701-5715.

    114. Hereditary semigroup algebras" (with E. Jespers), Journal of Algebra 233 (2000), no. 1, 409--424. (Correction by the editor) and Journal of Algebra 229 (2000), 532--546.

       

      ·  Ph. D. Thesis. Hereditary Semigroup Rings and Maximal Orders.