Commutation with codes

Commutation with codes

The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...

On Commutation and Primitive Roots of Codes

Quantum error correcting codes and Weyl commutation relations

This is mainly an expository account of the general theory of quantum error correcting codes exploiting the commutation relations between the Weyl operators associated with a finite additive abelian group. There are some new elements of proofs and remarks, particularly, in the context of the Knill-Laflamme theorem [5].

Commutation Structures

For fixed object X in a monoidal category, an X-commutation structure on an object A is just a map X⊗A → A⊗X. We study aspects of such structures in case A has a dual object. We consider a monoidal category V,⊗, I; for simplicity we let it be strict (the application we have in mind is anyway a category of endofuncors on a category, with composition as ⊗). Let X be an object in V, fixed througho...

A quadratic buck converter with lossless commutation

High switching frequency associated with soft commutation techniques is a new trend in switching converters. Following this trend, the authors present a buck pulsewidth modulation converter, where the dc voltage conversion ratio has a quadratic dependence on duty cycle, providing a large step-down. By introducing two resonant networks, soft switching is attained, providing highly efficient oper...