48 research outputs found
About a class of Hadamard propelinear codes
This article aims to explore the algebraic structure of Hadamard propelinear codes, which are not abelian in general but they have good algebraic and combinatorial properties. We construct a subclass of Hadamard propelinear codes which enlarges the family of the Hadamard translation invariant propelinear codes. Several papers have been devoted to the relations between difference sets, t-designs, cocyclic-matrices and Hadamard groups, and we present a link between them and a class of Hadamard propelinear codes, which we call full propelinear. Finally, as an exemplification, we provide a full propelinear structure for all Hadamard codes of length sixteen
On the number of nonequivalent propelinear extended perfect codes
The paper proves that there exist an exponential number of nonequivalent
propelinear extended perfect binary codes of length growing to infinity.
Specifically, it is proved that all transitive extended perfect binary codes
found by Potapov are propelinear. All such codes have small rank, which is one
more than the rank of the extended Hamming code of the same length. We
investigate the properties of these codes and show that any of them has a
normalized propelinear representation
Quasi-Hadamard Full Propelinear Codes
In this paper, we give a characterization of quasi-Hadamard groups in terms of propelinear codes. We
define a new class of codes that we call quasi-Hadamard full propelinear codes. Some structural properties of
these codes are studied and examples are provided.Junta de Andalucía FQM-016Ministerio de Economía y Competitividad TIN2016-77918-