Codes in Dihedral Group Algebra

Non-commutative convolutional codes over the infinite dihedral group

Classic convolutional codes are defined as the convolution of a message and a transfer function over Z. In this paper, we study convolutional codes over the infinite dihedral group D∞. The goal of this study is to design convolutional codes with good and interesting properties and intended to be more resistant to code recognition. Convolution of two functions on D∞ corresponds to the product of...

LDPC codes: a group algebra formulation

The Generalized Reed-Muller codes in a modular group algebra

First we study some properties of the modular group algebra Fpr [G] where G is the additive group of a Galois ring of characteristic pr and Fpr is the field of p r elements. Secondly a description of the Generalized Reed-Muller codes over Fpr in Fpr [G] is presented.

Block-Coded PSK Modulation Using Two-Level Group Codes Over Dihedral Groups

A length n group code over a group G is a subgroup of G under component-wise group operation. Group codes over dihedral groups DM , with 2M elements, that are two-level constructible using a binary code and a code over ZM residue class integer ring modulo M , as component codes are studied for arbitrary M . A set of necessary and sufficient conditions on the component codes for the two-level co...

Symmetry classes of polynomials associated with the dihedral group

‎In this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎Then we discuss the existence of o-basis‎ ‎of these classes‎.