Abstract— We transpose the theory of rank metric and Gabidulin codes to the case of fields which are not finite fields. The Frobenius automorphism is replaced by any element of the Galois group of a cyclic algebraic extension of a base field. We use our framework to define Gabidulin codes over the field of rational functions using algebraic function fields with a cyclic Galois group. This gives...

A competitive rent-seeking club (CRSC) offers its members the chance of winning a prize (status, position, privilege) by being selected, typically, by a civil servant or a politician. The selector replaces in our setting the usual contest success function; instead of determining the winner on the basis of the club-members' efforts, he selects the winner on the basis of quality. This paper focus...

Convolutional codes have been widely used in several kinds of communication systems because of its excellent coding gain. Recently, the coded TPSK (Ternary phase shift keying) scheme has been proposed and it was shown that the scheme has attractive features for mobile communication systems; excellent bit error characteristics and small amount of amplitude fluctuation. The latter feature is very...

In this correspondence, the trellis representation of the Kerdock and Delsarte–Goethals codes is addressed. It is shown that the states of a trellis representation of DG(m; ) under any bit-order are either strict-sense nonmerging or strict-sense nonexpanding, except, maybe, at indices within the code’s distance set. For 3 and for m 6, the state complexity, smax[DG(m; )], is found. For all value...

COVER ARTICLE Lee et al. A quartz nanopillar hemocytometer for high-yield separation and counting of CD4+ T lymphocytes FEATURE ARTICLE Virgili et al. Confocal ultrafast pump–probe spectroscopy: a new technique to explore nanoscale composites Series Editors: Harry Kroto FRS, Florida State University, USA Paul O’Brien Manchester University, UK Ralph Nuzzo University of Illinois at UrbanaChampaig...

In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe the algebraic parameters of the codes in a more accessible way. We show that the existence of such codes with given algebraic parameters can be reduced to the...

Rotationally invariant trellis codes often are of significant importance for fast and easy receiver synchronization and acquisition. With the help of 2-dimensional symbol constellations new 8PSK trellis codes are presented that are rotationally invariant to phase shifts by multiples of a/4 without an increase in complexity over noninvariant codes. (1 -dimensional coding: 1D-coding). Recently tr...

l . INTRODUCTION A class of double error correcting linear convolutional codes are given. T h e codes are derived from double-error-correct ing tr iple-error-detect ing extended BCH codes. T h e codes being proposed are not covered by previous works ([7], [2], [3]). Error propagation in the proposed codes is discussed. For the sake of simplicity of arguments only binary codes are discussed. Ext...

It is well known that a convolutional code can be viewed as a linear system over a nite eld. In this paper we develop this viewpoint for convolutional codes using several recent innovations from the systems theory literature. In particular we deene codes as behaviors of a set of compact support time trajectories over a vector space. We also consider several diierent representations of codes, in...