Publications

Most of the pdf files in this list are preprints and might differ from the published version of the paper.

with S. Linton, A. Niemeyer, R. Parker, J. Thackray: A parallel algorithm for Gaussian elimination over finite fields (submitted)

Unitary discriminants of characters (submitted)

with Tobias Braun Orthogonal representations of SL2(q) in defining characteristic (Beitraege zur Algebra und Geometrie, to appear)

Symmetrizations of quadratic and hermitian forms. J. Algebraic Combinatorics 61, article 29 (2025)

with Thomas Breuer and Richard Parker An Atlas of Orthogonal Representations in The Computer Algebra System OSCAR, edited by Wolfram Decker, Christian Eder, Claus Fieker, Max Horn, Michael Joswig, AACIM, volume 32, Springer International Publishing 2025.

with Marvin Anas Hahn, Mima Stanojkovski, and Bernd Sturmfels Subspaces Fixed by a Nilpotent Matrix (Orbita Mathematicae, Vol. 1, No. 1, 2024, 1-15)

with Linda Hoyer Orthogonal Determinants of SL3(q) and SU3(q). Archiv der Mathematik 121 (2023) SharedIt

with Leonie Scheeren Gamma-conjugate weight enumerators and invariant theory. Archiv der Mathematik 121 (2023) SharedIt

with Yassine El Maazouz and Mima Stanojkovski Bolytrope orders. Int. J. Number Theory 19 (2023) 937--954.
online first

with Tsuyoshi Miezaki Pseudo-normalized Hecke eigenform and its application to extremal 2-modular lattices. J. Number Theory 248 (2023) 294--309.

with Richard Parker Equivariant quadratic forms in characteristic 2. Bulletin LMS 55 (2023) 668--679

with Ghislain Fourier Degenerate flag varieties in network coding. Advances in Mathematics of Communications 17 (2023) 888--899 online first

with Richard Parker Orthogonal Stability. J. Algebra 614, 362--391 (2023).

On orthogonal discriminants of characters. Albanian J. Math. Vol. 16. (2022), No. 1, 41-49.

Orthogonal determinants of characters. Archiv der Mathematik 119, 19-26 (2022)

with Markus Kirschmer Binary Hermitian lattices over number fields. Experimental Mathematics, Volume 31, Issue 1, 280-301 (2022)

with Yassine El Maazouz, Marvin Anas Hahn, Mima Stanojkovski, and Bernd Sturmfels Orders and Polytropes: Matrix Algebras from Valuations. Beitr Algebra Geom (2021).

On free elementary ZpCp lattices. Archiv der Mathematik 116 (2021), no. 5, 509-514.

Automorphisms of modular lattices. J. Pure and Applied Algebra 225 (2021), no. 7, 106606, 13 pp.

with Sihuang Hu Strongly perfect lattices sandwiched between Barnes-Wall lattices Journal LMS 101 (2020) 1068--1089

with Simon Eisenbarth Self-dual codes over chain rings. Math.Comput.Sci. 14, 443--456 (2020).

Frederico Pellarin, with an appendix by G.N. On extremal quasi-modular forms after Kaneko and Koike Kyushu J. of Math. 74 (2020) 401--413

with Sihuang Hu Low dimensional strongly perfect lattices IV: The dual strongly perfect lattices of dimension 16. J. Number Theory 208 (2020), 262-294.

with Renaud Coulangeon Slopes of Euclidean lattices, tensor product and group actions. Israel Journal of Mathematics (2020) 39--61.

On conjugacy of diagonalizable integral matrices. Albanian J. Mathematics 13 (2019) 211--218.

with Markus Kirschmer Quaternary quadratic lattices over number fields. Int. J. Number Theory 15 (2019) 309--325.

with Dirk Liebhold and Angeles Vazquez Castro
Generalizing subspace codes to flag codes using group actions.
in Network coding and subspace designs, 67--89, Signals Commun. Technol., Springer, Cham, 2018.

with Dirk Liebhold and Angeles Vazquez Castro Network coding with flags. Des. Codes Cryptogr. 86 (2018) 269-284.

with Markus Kirschmer One class genera of lattice chains over number fields. in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory Herausgeber: G. Böckle, W. Decker, G. Malle. Springer (2017) 503-532.

with Sarah Rees and Richard Parker A method for building permutation representations of finitely presented groups. Contemporary Mathematics 694 (2017) 177-192. (Proceedings of the conference Finite Simple Groups: Thirty Years of the Atlas and Beyond edited by Manjul Bhargava, Robert Guralnick, Gerhard Hiss, Klaus Lux and Pham Huu Tiep.)

Computing with arithmetic groups (Abstract of invited talk) Proceedings of the ISSAC 2017, Kaiserslautern)

with Oliver Braun The orthogonal character table of SL2(q) J. Algebra 486 (2017) 64-79.
Note that the lines for q=3 mod 8 and q=7 mod 8 (character degree q+1) need to be interchanged in the table of Theorem 4.2. This can be seen from the computation of the real Clifford invariant, which is non-trivial if q=3 mod 8 and trivial for q=7 mod 8.

with Dirk Liebhold Automorphism groups of Gabidulin-like codes.
Archiv der Mathematik 107 (2016) 355-366.

with Sihuang Hu There is no [24,12,9] doubly-even self-dual code over F4.
Advances in Mathematics of Communication 10 (2016) 583-588

with Wolfgang Willems On self-dual MRD codes.
Advances in Mathematics of Communication 10 (2016) 633-642

Automorphisms of extremal unimodular lattices in dimension 72.
Journal of Number Theory (2016) 362--383
link to the published version

with Amy Feaver, Anna Haensch, and Jingbo Liu
Kneser-Hecke-operators for codes over finite chain rings in
Directions in Number Theory, Proceedings of the 2014 WIN3 Workshop, edited by Ellen E. Eischen, Ling Long, Rachel Pries, and Katherine Stange, Springer International Publishing Switzerland 2016

with O. Braun, R. Coulangeon, S. Schönnenbeck
Computing in arithmetic groups with Voronoi's algorithm.
Journal of Algebra 435 (2015) 263--285
Database for unit groups of orders

with Martino Borello
On involutions in extremal self-dual codes and the dual distance of semi self-dual codes.
Finite fields and their applications (2015) 80--89

with R. Coulangeon
Maximal finite subgroups and minimal classes.
L'Enseignement Math 60 (2014) 231--246

with A. Schaefer
A nilpotent non abelian group code.
Algebra and Discrete Mathematics 18 (2014) 268-273

A fourth extremal even unimodular lattices of dimension 48
Discrete Mathematics (2014) 133-136
Correction: There is a factor 2 missing in the order of the automorphism group of P48p, the structure of the group is given correctly. I thank Christoph Keller (ETH Zürich) for pointing out this error.

with R. Parker
On extremal even unimodular 72-dimensional lattices.
Math. Comp. 83 (2014), no. 287, 1489-1494.
Explicit bases of the sublattices described in the paper may be found here.

with Darwin Villar An analogue of the Pless symmetry codes.
Proceedings OC 2013

On automorphisms of extremal even unimodular lattices.
Int. J. Number Theory Vol. 9 (2013) 1933-1959
Correction: There is a factor 2 missing in the order of the automorphism group of P48p, the structure of the group is given correctly. I thank Christoph Keller (ETH Zürich) for pointing out this error.
The version on my homepage contains a more detailed proof of Corollary 4.11

with E. Nossek and B. Venkov
Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15.
J. Théorie de nombres de Bordeaux 25 (2013) 147-161

with M. Borello and F. Dalla Volta
The automorphism group of a self-dual [72,36,16] code does not contain S3, A4, or D8.
Advances in Mathematics of Communications 7 (2013) 503-510

with A. Krieg, M. Hentschel and A. Henn
On the classification of Eisenstein lattices which are even unimodular Z-lattices of rank 32.
International Journal of Mathematics and Mathematical Sciences vol. 2013, 4 pages, 2013. doi:10.1155/2013/837080.

with Sarah Chisholm, Alyson Deines, Ling Long, and Holly Swisher
p-adic analogues of Ramanujan type formulas for $1/\pi$
Mathematics 2013, 1, 9-31; doi:10.3390/math1010009

Golden lattices
in Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, Contemporary Mathematics, vol. 587, Amer. Math. Soc., Providence, RI, 2013, pp. 157-165.

with R. Coulangeon
Dense lattices as Hermitian tensor products.
in Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, Contemporary Mathematics, vol. 587, Amer. Math. Soc., Providence, RI, 2013, pp. 47-57.

Boris Venkov's work on lattices and spherical designs
in Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, Contemporary Mathematics, vol. 587, Amer. Math. Soc., Providence, RI, 2013, pp. 1-19.

On extremal lattices in jump dimensions
Correction: There is a factor 2 missing in the order of the automorphism group of P48p, the structure of the group is given correctly. I thank Christoph Keller (ETH Zürich) for pointing out this error.
Oberwolfach Reports, Optimal and Near Optimal Configurations on Lattices and Manifolds, August 2012

An even unimodular 72-dimensional lattice of minimum 8.
J. Reine und Angew. Math. 673 (2012) 237-247.

with T. Feulner The automorphism group of an extremal [72,36,16] code does not contain Z7, Z3xZ3, or D10.
IEEE Transactions on Information Theory 58 (11) 2012, 6916-6924.

with A. Krieg and M. Hentschel
On the classification of even unimodular Z-lattices with a complex structure.
Int. J. Number Theory 8 (2012) 983-992

with B. Venkov On tight spherical designs.
Algebra i Analiz 24 (2012) 163-171.

On extremal self-dual ternary codes of length 48
International Journal of Combinatorics, vol. 2012

An extremal [72,36,16] binary code has no automorphism group containing Z2xZ4, Q8, or Z10.
Finite Fields and Their Applications 18 (2012) 563-566

A generalisation of Turyn's construction of self-dual codes
Invited paper for the proceedings of the RIMS workshop: Research into vertex operator algebras, finite groups and combinatorics, Kyoto, Dec. 2010

with C. Bracken, E. Byrne, G. McGuire,
On the equivalence of quadratic APN functions
Designs, Codes and Cryptography 61 (2011) 261-272

Dichte Kugelpackungen
in Facettenreiche Mathematik, Herausgeberinnen: A. Werner, K. Wendland, Vieweg (2011).

with A. Krieg and M. Hentschel
On the classification of Eisenstein lattices which are even unimodular Z-lattices.
Abh. Math. Semin. Univ. Hambg. 80 (2010), no. 2, 183--192

with S. Böcherer
On theta series attached to maximal lattices and their adjoints.
J. Ramanujan Math. Soc. 25 (2010), no. 3, 265--284

with Boris Venkov
Low dimensional strongly perfect lattices. III: Dual strongly perfect lattices of dimension 14.
Int. J. Number Theory 6 (2010), no. 2, 387-409

with Allan Steel
Recognition of Division Algebras
J. Algebra 322 (2009) 903-909.
Magma program to calculate the Rational Schur Index of an algebra with uniformly distributed invariants
corrected version from May 6 2009 (we thank Bernd Souvignier for testing this function)
Input file to create some examples as cyclic orders

with Annika Günther
Automorphisms of doubly-even self-dual binary codes.
Bull. Lond. Math. Soc. 41 (2009), no. 5, 769-778.

with Michael Hentschel
Hermitian modular forms congruent to 1 modulo p.
Archiv der Mathematik (Basel) 92 (2009), no. 3, 251--256.

Finite Weil-representations and associated Hecke-algebras.
J. Number Theory 129 (2009), no. 3, 588--603.

with Christine Bachoc, Fernando Mario de Oliveira Filho, and Frank Vallentin
Lower bounds for measurable chromatic numbers.
Geom. Funct. Anal. 19 (2009), no. 3, 645–661

with B. Venkov
On lattices whose minimal vectors form a 6-design.
European J. Combin. 30 (2009), no. 3, 716--724.

with Annika Günther
Clifford-Weil groups for finite group rings, some examples.
Alb. J. Math. 2 (2008) 185-198

with Annika Günther and E.M. Rains
Clifford-Weil groups of quotient representations
Alb. J. Math. 2 (2008) 159-169

Self-dual codes and invariant theory.
(notes of three lectures given at the conference "New challenges in digital communications", Vlora, 28.4.-9.5.2008)
(for the slides of the talks click here.)

with Chaoping Xing
A Gilbert-Varshamov Type Bound for Euclidean Packings.
Math. Comp. 77 (264), 2339-2344 (2008)
Magma file calculating the bounds arising from the Leech lattice and an extremal even unimodular 72-dimensional lattice.

with K. Schindelar
S-extremal strongly modular lattices.
J. Théorie de nombres de Bordeaux 19 (2007) 683-701.

with E.M. Rains and N.J.A. Sloane
Self-dual codes and invariant theory.
(ACM volume 17, Springer 2006)

Kneser-Hecke-operators in coding theory.
Abh. Math. Sem. Univ. Hamburg 76 (2006) 79-90

with B. Venkov
Low dimensional strongly perfect lattices. I: The 12-dimensional case.
L'Enseignement Mathématiques 51 (2005) 129-163

with E. Bayer-Fluckiger
On the Euclidean minimum of some real number fields.
J. Théorie de nombres de Bordeaux 17 (2005) 437-454

with M. Teider
Hecke actions on certain strongly modular genera of lattices.
Archiv der Mathematik 84 (1) (2005) 46-56

On the radical idealizer chain of symmetric orders.
J. Algebra 283 (2) 622-638 (2005)

On blocks with cyclic defect group and their head orders.
Communications in Algebra 33 (3) 689 - 708 (2005)

Book Review
Jacques Martinet: Perfect lattices in Euclidean spaces.
Bull. Amer. Math. Soc. 41 (2004) 529-533.

with E. Rains and N. Sloane
Codes and invariant theory
Mathematische Nachrichten 274-275, 104-116 (2004)

with C. Bachoc Siegel modular forms, Grassmannian designs, and unimodular lattices.
Proceedings of the Algebraic Combinatorics Conference (Kumamoto, 2002).

Strongly modular lattices with long shadow.
J. Th. des Nombres de Bordeaux 16 (2004) 187-196.
on p. 190 there is a minus sign missing in the formula for s2 for N = 6 and 14.

with H.-G. Quebbemann, E. M. Rains and N. J. A. Sloane
Complete weight enumerators of generalized doubly even self-dual codes.
Finite fields and their applications, 10 (2004) 540-550.
Note that the proof that there is no doubly-even euclidean self-dual [24,12,9] code over F4 is wrong. There are two possible weight enumerators of such codes, one of which (with F2-rational subcode of dimension 4) is easily excluded. The paper with Sihuang Hu closes the gap by showing that the minimum distance of a doubly-even euclidean self-dual code of length 24 over F4 is at most 8.

with M. Hertweck On Group Ring Automorphisms.
Algebras and Representation Theory 7 (2) (2004), 189-210.

with B. Gross
Globally maximal arithmetic groups
J. Algebra 272 (2004), no. 2, 625-642.

with M. Künzer Elementary divisors of Gram matrices of certain Specht modules.
Comm. Alg. 31 (7) (2003) 3377 - 3427

Even lattices with covering radius stricktly smaller than sqrt{2}.
Beiträge zur Algebra und Geometrie, Vol. 44, No. 1, 2003, 229-234
Note that I forgot the case R=A2A1A1 in Theorem 7. This root system yields two further lattices, one with covering radius =sqrt{2} and one with c.r. strictly smaller than sqrt{2}

with B. Venkov Unimodular lattices with long shadow.
(Corrected version, we thank J. Martinet for pointing out an error in Section examples.)
J. Number Theory 99 (2003) 307-317

Gitter und Modulformen.
Survey article based on talk given at the 2002 DMV meeting in Halle.
Jahresbericht der DMV, 104. Band (2002), Heft 3, 123-142.

Group rings of finite groups over p-adic integers, some examples
Proceedings of the conference Around Group rings (Edmonton) Resenhas 5 (2002), no. 4, 329--350.

with C. Bachoc and R. Coulangeon Designs in Grassmannian spaces and lattices.
Journal of Algebraic Combinatorics 16 (1) 5-19 (2002).

with C. Bachoc Zonal functions for the unitary groups and applications to hermitian lattices.
J. Number Theory 96, 55-75 (2002)

with C. Bachoc and B. Venkov Odd unimodular lattices of minimum 4.
Acta Arithmetica 101, 151-158 (2002)

The principal block of Z_pS_2p
J. Group Theory 5 (2002) 2, 163-176.

with H. Koch and C. Gohlisch Block squares
Math. Nachrichten 241, 73-102 (2002)

with E. M. Rains and N. J. A. Sloane A Simple Construction for the Barnes-Wall Lattices
in Codes, Graphs, and Systems: A Celebraton of the Life and Career of G. David Forney, Jr. on the Occasion of his Sixtieth Birthday edited by R. E. Blahut and R. Koetter, Kluwer 2002, 333-342.

with P. Abramenko Lattice chain models for affine buildings of classical type.
Mathematische Annalen 322 (2002) 3, 537-562.

with E. M. Rains and N. J. A. Sloane The Invariants of the Clifford Groups
Designs, Codes, and Cryptography 24 (1), 99-122 (2001)

with B. Venkov On Siegel modular forms of weight 12.
J. reine und angew. Mathematik 531, 49-60 (2001)

with B. Venkov The strongly perfect lattices of dimension 10.
J. Théorie de Nombres de Bordeaux 12 (2000) 503-518
for related papers see home page of J. Martinet

On the cokernel of the Witt decomposition map.
J. Théorie de Nombres de Bordeaux 12 (2000) 489-501

Invariants of orthogonal G-modules from the character table.
Exp. Math. 9 (2000) 623-630

Faktorisieren ganzer Zahlen.
DMV Jahresbericht 102 (2000) 1-14.

The group ring of SL(2,p^f) over p-adic integers for p odd.
J. Algebra 230, 424-454 (2000)

The group ring of SL(2,2^f) over 2-adic integers.
J. reine und angew. Mathematik 528, 183-200 (2000)
pdf-file of a poster describing the strategie to determine the group rings of the groups SL(2,k).

Orthogonal Frobenius reciprocity.
J. Algebra 225, 250-260 (2000)

Orthogonale Darstellungen endlicher Gruppen und Gruppenringe Habilitationsschrift (RWTH Aachen)
Aachener Beiträge zur Mathematik 26 (1999) Verlag Mainz, Aachen

Construction and investigation of lattices with matrix groups
in Myung-Hwan Kim, John S. Hsia, Y. Kitaoka, R. Schulze-Pillot (Ed.) {\it Integral Quadratic Forms and Lattices}, Contemporary Mathematics 249 (1999) p. 205-220

The root lattices of the complex reflection groups
J. Group Theory 2.1 (1999) 15-38.

The group ring of SL(2,p²) over the p-adic integers
J. Algebra 210, 593-613 (1998)

The structure of maximal finite primitive matrix groups
in B.H. Matzat, G.-M. Greuel, G. Hiss (Eds.) Algorithmic Algebra and Number Theory (Springer, 1998) p. 417-422.

with A.M. Cohen, W. Plesken Maximal integral forms of the algebraic group G2 defined by finite subgroups.
J. Number Theory 72 (1998) 282-308

Finite quaternionic matrix groups.
Represent. Theory 2 (1998) 106-223

Some cyclo quaternionic lattices.
J. Algebra 199, 472-498 (1998)

with C.Bachoc Extremal lattices of minimum 8 related to the Mathieu group M22.
J. reine angew. Mathematik, 494 (1998), 155-171

The normaliser action and strongly modular lattices.
L'Ens. Math., 43 (1997) 67-76

with C.Bachoc Classification of two genera of 32-dimensional lattices over the Hurwitz order.
Exp. Math., Vol 6 (1997) No. 2, 151-162

Finite subgroups of GL(n,Q) for 25 <= n <=31.
Comm. Algebra 24 (7) (1996), 2341-2397.

Finite subgroups of GL(24,Q).
Exp. Math. Vol. 5, Number 3 (1996), 163-195.

with B. B. Venkov Non-existence of extremal lattices in certain genera of modular lattices.
J. Number Theory, Vol. 60, No. 2, October 1996. (310-317)

with A. Cohen, W. Plesken Cayley orders.
Compositio Mathematica 103: 63-74, 1996.

Endliche rationale Matrixgruppen vom Grad 24.
Dissertation RWTH Aachen (1995), Aachener Beiträge zur Mathematik 12 (1995) Verlag der Augustinus Buchhandlung, Aachen

with W. Plesken Finite rational matrix groups. and Finite rational matrix groups of degree 16.
AMS-Memoir No. 556, vol. 116 (1995). (144 pages)

with H. Koch Extremal even unimodular lattices of rank 32 and related codes.
Math. Nachr. 161 (1993), 309-319

Appendix of H. Koch, B.B. Venkov, Über gerade unimodulare Gitter der Dimension 32, III
Math. Nachr. 152 (1991), 191-213 (4 pages)

Wiedererkennung von Gittern. Diplomarbeit, Lehrstuhl B f. Mathematik, RWTH Aachen. (108 pages)