Juergen B.

Juergen Bierbrauer

Department of Mathematical Sciences
Michigan Technological University
1400 Townsend Drive, 226B Fisher Hall
Houghton, MI 49931-1295, U.S.A.
Phone:  (906) 487 3362
Fax: (906) 487 3133
E-mail: jbierbra@mtu.edu

book_small My book:

Introduction to Coding Theory
appeared in 2004

Publisher: Chapman & Hall/CRC

I am on the Editorial Board of Designs, Codes and Cryptography.

Mathematical Interests

My interest is in Discrete Mathematics: coding theory, finite geometries, algebra.

List of publications

Here it is

Coding Theory ...

A family of highly symmetric codes (coauthors S. Marcugini, F. Pambianco)

(a slightly extended version of what appeared in the IEEE IT Transactions, October 2005)

New codes via the lengthening of BCH codes with UEP codes , (coauthors Yves Edel and Ludo Tolhuizen).

A family of 2-weight codes related to BCH-codes , (coauthor Yves Edel).

New code parameters from Reed Solomon subfield codes , (coauthor Yves Edel).

Extending and lengthening BCH-codes , (coauthor Yves Edel).

Lengthening and the Gilbert-Varshamov bound , (coauthor Yves Edel).

Some codes related to BCH-codes of low dimension , (coauthor Yves Edel).

Inverting construction Y1 , (coauthor Yves Edel).

Parameters for binary codes , (coauthor Yves Edel).

Parameters for ternary codes , (coauthor Yves Edel).

Parameters for quaternary codes , (coauthor Yves Edel).

New code parameters ,

The structure of some good codes ,

... in particular additive/quantum codes

A geometric non-existence proof of an extremal additive code (coauthors S.Marcugini, F.Pambianco)

Geometric Constructions of Quantum Codes (coauthors D.Bartoli, S.Marcugini, F.Pambianco)

The spectrum of stabilizer quantum codes of distance 3

The geometry of quantum codes (coauthors G. Faina, M. Giulietti, S. Marcugini, F. Pambianco)

Short additive quaternary codes (coauthors E. Edel, G. Faina, S. Marcugini, F. Pambianco)

Additive quaternary codes of small length (coauthors G. Faina, S. Marcugini, F. Pambianco)

Cyclic additive and quantum stabilizer codes

Quantum twisted codes (coauthor Yves Edel).

Direct constructions of additive codes

The theory of cyclic codes and a generalization to additive codes

... and further Applications

Constructing good covering codes for applications in Steganography (coauthor Jessica Fridrich)

Universal hashing and geometric codes

Authentication via algebraic-geometric codes

Dense sphere packings from new codes, (coauthor Yves Edel).

Orthogonal arrays and the like

Construction of orthogonal arrays

Theory of perpendicular arrays (coauthor Yves Edel).

APN functions and crooked functions

A family of crooked functions

Crooked binomials (coauthor Gohar Kyureghyan).

Planar functions and semifields

New semifields, PN and APN functions

New commutative semifields and their nuclei .

Limited bias, weak dependence, covering arrays and cryptologic applications

Constructive asymptotic lower bounds on linear codes and weakly biased arrays (coauthor Holger Schellwat).

Efficient constructions of $\epsilon -$biased arrays, $\epsilon -$dependent arrays and authentication codes (coauthor Holger Schellwat).

Weakly biased arrays, weakly dependent arrays and error-correcting codes (coauthor Holger Schellwat).

Almost independent and weakly biased arrays: efficient constructions and cryptologic applications (coauthor Holger Schellwat).

Galois geometries

A family of caps in projective $4$-space in odd characteristic (coauthor Yves Edel).

Recursive constructions for large caps (coauthor Yves Edel).

$41$ is the largest size of a cap in $PG(4,4)$(coauthor Yves Edel).

The maximal size of a $3$-arc in $PG(2,8).$

Large caps in small spaces (coauthor Yves Edel).

Caps on classical varieties and their projections (coauthors Antonello Cossidente and Yves Edel).

The largest cap in $AG(4,4)$ and its uniqueness (coauthor Yves Edel).

Caps of order $3q^2$ in affine $4$-space in characteristic $2$ (coauthor Yves Edel).

The sporadic $A_7$-geometry and the Nordstrom-Robinson code

Large caps: A survey

Material on (t,m,s)-nets

Construction of digital nets from BCH-codes , (coauthor Yves Edel).

Families of ternary (t,m,s)-nets related to BCH-codes , (coauthor Yves Edel).

Good binary nets

Good ternary nets

Good nets in other characteristics

Coding-theoretic constructions for $(t,m,s)$-nets and ordered orthogonal arrays (coauthors Yves Edel and W. Ch. Schmid)

A family of binary $(t,m,s)$-nets of strength $5,$ (coauthor Yves Edel)

An asymptotic Gilbert-Varshamov bound for tms-nets (coauthor Wolfgang Schmid)

Families of nets of low and medium strength (coauthor Yves Edel)

A little $(t,m,s)$-bibliography


A direct approach to linear programming bounds

Bounds on affine caps (coauthor Yves Edel).

Bounds on orthogonal arrays and resilient functions

A note on the duality of linear programming bounds for orthogonal arrays and codes (coauthors K.Gopalakrishnan, D.R.Stinson).

Orthogonal Arrays, Resilient Functions, Error Correcting Codes and Linear Programming Bounds (coauthors K.Gopalakrishnan, D.R.Stinson).

Combinatorial Designs

An infinite family of $7$-designs

Projective planes, coverings and a network problem (coauthors S. Marcugini and F. Pambianco)

Some friends of Alltop's designs

A family of 4-designs with block-size 9

A new family of 4-designs

Lecture Notes

MA5301: Finite groups and fields (Fall 2008)

MA3210: Introduction to Combinatorics

MA 4211: Information Theory/ Data Compression

Partition identities

MA 462: Introduction to Group Theory

MA 5980: Finite Geometries

Group Theory and Applications (lecture 2005)

Groups and Geometries

Introduction to Group Theory and Applications (lecture 2000)

MA 572,COMBINATORICS II:Permutation groups, designs and enumeration

More information is on Yves Edel's homepage.

Here is the link to MinT, the Salzburg database for net parameters

And here a link to A.E.Brouwer's data base of bounds for linear codes.