scholarly journals On one-lee weight and two-lee weight $ \mathbb{Z}_2\mathbb{Z}_4[u] $ additive codes and their constructions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jie Geng ◽  
Huazhang Wu ◽  
Patrick Solé
Keyword(s):  
Gray Map ◽  
Weight Enumerator ◽  
Lee Weight ◽  
Construction Methods ◽  
Additive Codes ◽  
Type Identity

<p style='text-indent:20px;'>This paper mainly study <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes. A Gray map from <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{Z}_{2}^{\alpha}\times\mathbb{Z}_{4}^{\beta}[u] $\end{document}</tex-math></inline-formula> to <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{Z}_{4}^{\alpha+2\beta} $\end{document}</tex-math></inline-formula> is defined, and we prove that is a weight preserving and distance preserving map. A MacWilliams-type identity between the Lee weight enumerator of a <inline-formula><tex-math id="M5">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive code and its dual is proved. Some properties of one-weight <inline-formula><tex-math id="M6">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes and two-weight projective <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes are discussed. As main results, some construction methods for one-weight and two-weight <inline-formula><tex-math id="M8">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes are studied, meanwhile several examples are presented to illustrate the methods.</p>

scholarly journals Codes with the same Lee weight enumerator are isometric

1982 ◽  
Vol 32 (3) ◽  
pp. 405-406
Author(s):  
Donald Y Goldberg ◽  
Anita E Solow
Keyword(s):  
Weight Enumerator ◽  
Lee Weight

scholarly journals On ag-fold jointm-spotty Lee weight enumerator

2013 ◽  
Vol 313 (20) ◽  
pp. 2150-2161
Author(s):  
Anuradha Sharma ◽  
Amit K. Sharma
Keyword(s):  
Weight Enumerator ◽  
Lee Weight

FEW-WEIGHT CODES FROM TRACE CODES OVER

2018 ◽  
Vol 98 (1) ◽  
pp. 167-174
Author(s):  
MINJIA SHI ◽  
YUE GUAN ◽  
CHENCHEN WANG ◽  
PATRICK SOLÉ
Keyword(s):  
Secret Sharing ◽  
Infinite Family ◽  
Gray Map ◽  
Secret Sharing Schemes ◽  
Lee Weight ◽  
Trace Codes ◽  
Defining Sets

We construct two families of few-weight codes for the Lee weight over the ring $R_{k}$ based on two different defining sets. For the first defining set, taking the Gray map, we obtain an infinite family of binary two-weight codes which are in fact $2^{k}$-fold replicated MacDonald codes. For the second defining set, we obtain two infinite families of few-weight codes. These few-weight codes can be used to implement secret-sharing schemes.

scholarly journals Linear, cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 897-906
Author(s):  
Ödemiş Özger ◽  
Ümmü Kara ◽  
Bahattin Yıldız
Keyword(s):  
Linear Codes ◽  
Gray Map ◽  
Binary Codes ◽  
Constacyclic Codes ◽  
Weight Enumerators ◽  
Lee Weight ◽  
Macwilliams Identities

In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over S4 are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over S4.

Proposal for Refugee Housing in Southeast Europe Utilizing Regionally Appropriate, Sustainable, and Affordable Construction Methods

2020 ◽  
Vol 22 ◽  
Author(s):  
Hana Cicevic ◽  
Sarah Gamble
Keyword(s):  
Architectural Design ◽  
Housing Demand ◽  
Situational Factors ◽  
Housing Unit ◽  
Southeast Europe ◽  
Construction Methods ◽  
Permanent Housing ◽  
Emergency Housing ◽  
Communal Housing ◽  
Construction Model

This research focuses on the emergency-housing demand caused by the on-going refugee crisis in Southeastern Europe. The research and proposed solutions focus on Northern Serbia, as this region generally lacks permanent housing solutions for accommodating the increasing influx of immigrants. The outcome of this research is an architectural proposal for the refugee housing unit designed particularly for the situational factors of this focus region.    The study identifies earth architecture as the primary building technique, due to its ability to satisfy a range of defined end-product goals.  These goals include: the sustainability of the material, quality and durability of the final product, skill level required for non-professional construction, final cost of material and execution, historical regional precedent, and opportunity for communal engagement of the immigrant population. The proposed architectural design uses earth-bag construction as the sub-method most suitable for this location and in keeping with the goals outlined above. The proposed housing unit is a singular component that could be duplicated to create larger communal housing communities.  A broad overview of possible solutions is included, followed by the development of the earth-bag construction option. The development of this proposal includes material studies, sketches, and an architectural model as representation tools. The outcomes of this research serve as a guideline, rather than a precise construction model, in creating much needed refugee housing communities in North Serbia.      

DESIGN-BUILD: AN EFFECTIVE APPROACH FOR ARCHITECTURE STUDIO EDUCATION

2018 ◽  
Vol 12 (2) ◽  
pp. 146 ◽  
Author(s):  
Nabil Mohareb ◽  
Sara Maassarani
Keyword(s):  
Material Selection ◽  
Environmental Constraints ◽  
Design Project ◽  
Construction Methods ◽  
Physical Scale ◽  
Design Build ◽  
Simulation Results ◽  
Education Process ◽  
Real Target

Current architecture studios are missing an important phase in the education process, which is constructing the students’ conceptual ideas on a real physical scale. The design-build approach enables the students to test their ideas, theories, material selection, construction methods, environmental constraints, simulation results, level of space functionality and other important aspects when used by real target clients in an existing context. This paper aims to highlight the importance of using the design-build method through discussing a design project case study carried out by the Masters of Architecture design programme students at Beirut Arab University, who have built prototype units for refugees on a 1:1 scale.

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