New Hermitian self-dual MDS or near-MDS codes over finite fields

A linear code over a finite field is called Hermitian self-dual if the code is self-dual under the Hermitian inner-product. The Hermitian self-dual code is called MDS or near-MDS if the code attains or almost attains the Singleton bound. In this paper we construct new Hermitian self-dual MDS or near-MDS codes over and of length up to 14

Linear Continuous Sliding Mode-based Attitude Controller with Modified Rodrigues Parameters Feedback

This paper studies an attitude control system design based on modified Rodrigues parameters feedback. It employs a linear continuous sliding mode controller. The sliding mode controller is able to bring the existence of the sliding motion asymptotically. Besides, the attitude control system equilibrium point is proved to have an asymptotic stability guarantee through further analysis. This stability analysis is conducted since the sliding mode existence on the designed sliding surface does not imply the stability guarantee of the system's equilibrium. This paper ends with some numerical examples that confirm the effectiveness of the designed attitude control system

Asymptotic Stability of Quaternion-based Attitude Control System with Saturation Function

In the design of attitude control, rotational motion of the spacecraft is usually considered as a rotation of rigid body. Rotation matrix parameterization using quaternion can represent globally attitude of a rigid body rotational motions. However, the representation is not unique hence implies difficulties on the stability guarantee. This paper presents asymptotically stable analysis of a continuous scheme of quaternion-based control system that has saturation function. Simulations run show that the designed system applicable for a zero initial angular velocity case and a non-zero initial angular velocity case due to utilization of deadzone function as an element of the defined constraint in the stability analysis

PENGARUH DIAMETER PENGEROLAN DINGIN TERHADAP KEKUATAN BENDING BAJA KARBON RENDAH

Baja St 41 merupakan baja karbon rendah yang mengandung karbon dibawah 0,30% banyak diaplikasikan untuk konstruksi umum. Pembetukan benda dengan pengerolan banyak dilakukan untuk pembuatan bejana maupun konstruksi penguatan dengan plat baja .Pada penelitian ini dilakukan proses pengerolan dingin, baja AISI 1015 setebal 7,65 mm dengan radius: 500, 1000, 2000 dan 3000 mm. Pengujian yang dilakukan adalah uji komposisi kimia, uji kekerasan uji struktur mikro , dan uji kekuatan bending dengan arah berlawanan dari arah pengerolan. Dari hasil pengujian tersebut dapat disimpulkan bahwa pengerolan akan meningkatkan kekuatan bending sampai pada ukuran tertentu. Setelah Iewat batas tertentu maka bahan akan luluh sehingga menurunkan kekerasan serta kekuatan bendingnya.Kata kunci: Baja St 41, Rolling, Ferit, Kekuatan Bendin

Skew cyclic codes over Z4+vZ4\mathbb{Z}_4+v\mathbb{Z}_4 with derivation: structural properties and computational results

In this work, we study a class of skew cyclic codes over the ring $R:=\mathbb{Z}_4+v\mathbb{Z}_4,$ where $v^2=v,$ with an automorphism $\theta$ and a derivation $\Delta_\theta,$ namely codes as modules over a skew polynomial ring $R[x;\theta,\Delta_{\theta}],$ whose multiplication is defined using an automorphism $\theta$ and a derivation $\Delta_{\theta}.$ We investigate the structures of a skew polynomial ring $R[x;\theta,\Delta_{\theta}].$ We define $\Delta_{\theta}$-cyclic codes as a generalization of the notion of cyclic codes. The properties of $\Delta_{\theta}$-cyclic codes as well as dual $\Delta_{\theta}$-cyclic codes are derived. As an application, some new linear codes over $\mathbb{Z}_4$ with good parameters are obtained by Plotkin sum construction, also via a Gray map as well as residue and torsion codes of these codes.Comment: 25 page

A general family of Plotkin-optimal two-weight codes over Z4\mathbb{Z}_4

We obtain all possible parameters of Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4,$ together with their weight distributions. We show the existence of codes with these parameters as well as their weight distributions by constructing an infinite family of two-weight codes. Previously known codes constructed by Shi et al. (\emph{Des Codes Cryptogr.} {\bf 88}(3):1-13, 2020) can be derived as a special case of our results. We also prove that the Gray image of any Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4$ has the same parameters and weight distribution as some two-weight binary projective codes of type SU1 in the sense of Calderbank and Kantor (\emph{Bull. Lond. Math. Soc.} {\bf 18}:97-122, 1986).Comment: 17 pages, finlar versio