Let $mathbb{F}_q$ be a finite field of q elements, $R=mathbb{F}_q+umathbb{F}_q$ (u2=0) and D2n= be a dihedral group of order n. Left ideals of the group ring R[D2n] are called left dihedral codes over R of length 2n, and abbreviated as left D2n-codes over R. Let n be a positive factor of qe+1 for some positive integer e. In this paper, any left D2n-code over R is uniquely decomposed into a direct sum of concatenated codes with inner codes Ai and outer codes Ci, where Ai is a cyclic code over R of length n and Ci is a linear code of length 2 over a Galois extension ring of R. More precisely, a generator matrix for each outer code Ci is given. Moreover, a formula to count the number of these codes is obtained, the dual code for each left D2n-code is determined and all self-dual left D2n-codes over R are presented, respectively.

In this paper, we present a new extension of the butterfly digraph, which is known as one of the topologies used for interconnection networks. The butterfly digraph was previously generalized from binary to d-ary. We define a new digraph by adding a signed label to each vertex of the d-ary butterfly digraph. We call this digraph the dihedral butterfly digraph and study its properties. Furthermore, we show that this digraph can be represented as a Cayley graph. It is well known that a butterfly digraph can be represented as a Cayley graph on the wreath product of two cyclic groups [1]. We prove that a dihedral butterfly digraph can be represented as a Cayley graph in two ways.

This paper examines polarimetric scattering characteristics caused by a dihedral corner reflector of finite size. The dihedral corner reflector is a basic model of double-bounce structure in urban area. The detailed scattering information serves the interpretation of Polarimetric Synthetic Aperture Radar (POLSAR) data analysis. The Finite-Difference Time-Domain (FDTD) method is utilized for the scattering calculation because of its simplicity and flexibility in the target shape modeling. This paper points out that there exists a stable double-bounce squint angle region both for perfect electric conductor (PEC) and dielectric corner reflectors. Beyond this stable squint angular region, the scattering characteristics become completely different from the assumed response. A criterion on the double-bounce scattering is proposed based on the physical optics (PO) approximation. The detailed analyses on the polarimetric index (co-polarization ratio) with respect to squint angle and an experimental result measured in an anechoic chamber are shown.

Polarimetric calibration of radar is indispensable for using radar data effectively. This paper proposes a polarimetric radar calibration algorithm using polarization-preserving and polarization-selective reflectors as reference targets. The algorithm assumes radar antenna reciprocity but allows different co-polarization transmission characteristics between horizontal and vertical polarization channels. In processing, the second order terms of small cross-talk factors in antenna polarization transfer characteristics are ignored. The major advantage of the present algorithm is that it does not need assumptions on the scattering characteristics of the background natural surface and is independent of external phase calibration. The results of error analysis show that the present algorithm has sufficient tolerance against errors of reference targets. The validity of the present algorithm was evaluated by analyzing the Spaceborne Imaging Radar C (SIR-C) data and the results were satisfactory.