Twisted permutation codes

Permutation codes

There are many analogies between subsets and permutations of a set, and in particular between sets of subsets and sets of permutations. The theories share many features, but there are also big differences. This paper is a survey of old and new results about sets (and groups) of permutations, concentrating on the analogies and on the relations to coding theory. Several open problems are describe...

A generalization of quasi-twisted codes: Multi-twisted codes

Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this work we introduce a new generalization of QT codes that we call multi-twisted (MT) codes and study some of their basic properties. Presenting several methods o...

Quantum Twisted Codes

Generalised Twisted Gabidulin Codes

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.

Generalized Twisted Gabidulin Codes

Based on the twisted Gabidulin codes obtained recently by Sheekey, we construct a new family of maximal rank distance codes as a set of qpolynomials over Fqn , which includes the generalized Gabidulin codes and the twisted Gabidulin codes. Their Delsarte duals and adjoint codes are investigated. We also obtain necessary and sufficient conditions for the equivalence between two members of our ne...