Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

Polynomial Automorphisms Over Finite Fields

It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).

The Automorphism Group of the Free Algebra of Rank Two

The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group of linear automorphisms.

Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm

2000 Mathematics Subject Classification: 17A50, 05C05.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Some MDS Codes over Gf(64) Connected with the Binary Doubly-Even [72,36,16] Code

* The author is supported by a Return Fellowship from the Alexander von Humboldt Foundation.

On the Automorphism Groups of some AG-Codes Based on Ca;b Curves

*Partially supported by NATO.

Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.

New Binary Extremal Self-Dual Codes of Lengths 50 and 52

* This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995.

New Binary $[70,35,12]$ Self-Dual and Binary $[72,36,12]$ Self-Dual Doubly-Even Codes

∗ This work was supported in part by the Bulgarian NSF under Grant MM-901/99

Fermat's Equation in Matrices

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

On Extremal Binary Doubly-Even Self-Dual Codes of Length 88*

In this paper we present 35 new extremal binary self-dual doubly-even codes of length 88. Their inequivalence is established by invariants. Moreover, a construction of a binary self-dual [88, 44, 16] code, having an automorphism of order 21, is given.

A Method for Classification of Doubly Resolvable Designs and Its Application

This article presents the principal results of the Ph.D. thesis Investigation and classification of doubly resolvable designs by Stela Zhelezova (Institute of Mathematics and Informatics, BAS), successfully defended at the Specialized Academic Council for Informatics and Mathematical Modeling on 22 February 2010.

Involution Matrix Algebras – Identities and Growth

2000 Mathematics Subject Classification: 16R50, 16R10.

On Binary Self-Dual Codes of Length 62 with an Automorphism of Order 7

Николай Янков - Класифицирани са с точност до еквивалетност всички оптимални двоични самодуални [62, 31, 12] кодове, които притежават автоморфизъм от ред 7 с 8 независими цикъла при разлагане на независими цикли. Използвайки метода за конструиране на самодуални кодове, притежаващи автоморфизъм от нечетен прост ред е доказано, че съществуват точно 8 нееквивалентни такива кода. Три от получените кодове имат тегловна функция, каквато досега не бе известно да съществува.