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## Designs, Codes and Cryptography OnlineFirst articles

15.11.2017

### Flags of almost affine codes and the two-party wire-tap channel of type II

We describe a two-party wire-tap channel of type II in the framework of almost affine codes. Its cryptological performance is related to some relative profiles of a pair of almost affine codes. These profiles are analogues to relative generalized …

15.11.2017

### Fourier transforms and bent functions on finite groups

Let G be a finite nonabelian group. Bent functions on G are defined by the Fourier transforms at irreducible representations of G. We introduce a dual basis $${\widehat{G}}$$ G ^ , consisting of functions on G determined by its unitary irreducible …

15.11.2017

### Group rings, G-codes and constructions of self-dual and formally self-dual codes

We describe G-codes, which are codes that are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a G-code is also a G-code. We give constructions of self-dual …

14.11.2017

### On group codes with complementary duals

We investigate and characterize ideals in a group algebra KG which have complementary duals, i.e., ideals C in KG which satisfy $$KG = C \oplus C^\perp .$$ K G = C ⊕ C ⊥ . In the special case that G is a cyclic group we get an early result of Yang …

09.11.2017

### Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator

In this paper we revisit the modular inversion hidden number problem (MIHNP) and the inversive congruential generator (ICG) and consider how to attack them more efficiently. We consider systems of modular polynomial equations of the form …

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There is a great deal of activity in design theory, coding theory and cryptography and recently there has been considerable research done which brings together more than one of the subjects. Designs, Codes and Cryptography provides a forum for high quality papers of both a theoretical and a practical nature which bridge more than one of these areas, encouraging interaction between them. It emphasizes the algebraic and geometric aspects of design theory, coding theory and cryptography.

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