Commenced in January 2007
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Edition: International
Paper Count: 4

Search results for: Ederlina Nocon

4 A Characterization of Skew Cyclic Code with Complementary Dual

Authors: Eusebio Jr. Lina, Ederlina Nocon

Abstract:

Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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3 On the Construction of Some Optimal Binary Linear Codes

Authors: Skezeer John B. Paz, Ederlina G. Nocon

Abstract:

Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7.

Keywords: bounds of linear codes, Griesmer bound, construction of linear codes, optimal binary linear codes

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2 Non-Standard Monetary Policy Measures and Their Consequences

Authors: Aleksandra Nocoń (Szunke)

Abstract:

The study is a review of the literature concerning the consequences of non-standard monetary policy, which are used by central banks during unconventional periods, threatening instability of the banking sector. In particular, the attention was paid to the effects of non-standard monetary policy tools for financial markets. However, the empirical evidence about their effects and real consequences for the financial markets are still not final. The main aim of the study is to survey the consequences of standard and non-standard monetary policy instruments, implemented during the global financial crisis in the United States, United Kingdom and Euroland, with particular attention to the results for the stabilization of global financial markets. The study analyses the consequences for short and long-term market interest rates, interbank interest rates and LIBOR-OIS spread. The study consists mainly of the empirical review, indicating the impact of the implementation of these tools for the financial markets. The following research methods were used in the study: literature studies, including domestic and foreign literature, cause and effect analysis and statistical analysis.

Keywords: asset purchase facility, consequences of monetary policy instruments, non-standard monetary policy, quantitative easing

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1 Influence of the Location of Flood Embankments on the Condition of Oxbow Lakes and Riparian Forests: A Case Study of the Middle Odra River Beds on the Example of Dragonflies (Odonata), Ground Beetles (Coleoptera: Carabidae) and Plant Communities

Authors: Magda Gorczyca, Zofia Nocoń

Abstract:

Past and current studies from different countries showed that river engineering leads to environmental degradation and extinction of many species - often those protected by local and international wildlife conservation laws. Through the years, the main focus of rivers utilization has shifted from industrial applications to recreation and wildlife preservation with a focus on keeping the biodiversity which plays a significant role in preventing climate changes. Thus an opportunity appeared to recreate flooding areas and natural habitats, which are very rare in the scale of Europe. Additionally, river restoration helps to avoid floodings and periodic droughts, which are usually very damaging to the economy. In this research, the biodiversity of dragonflies and ground beetles was analyzed in the context of plant communities and forest stands structure. Results were enriched with data from past and current literature. A comparison was made between two parts of the Odra river. A part where oxbow lake and riparian forest were separated from the river bed by embankment and a part of the river with floodplains left intact. Validity assessment of embankments relocation was made based on the research results. In the period between May and September, insects were collected, phytosociological analysis were taken, and forest stand structure properties were specified. In the part of the river not separated by the embankments, rare and protected species of plants were spotted (e.g., Trapanatans, Salvinianatans) as well as greater species and quantitive diversity of dragonfly. Ground beetles fauna, though, was richer in the area separated by the embankment. Even though the research was done during only one season and in a limited area, the results can be a starting point for further extended research and may contribute to acquiring legal wildlife protection and restoration of the researched area. During the research, the presence of invasive species Impatiens parviflora, Echinocystislobata, and Procyonlotor were observed, which may lead to loss of the natural values of the researched areas.

Keywords: carabidae, floodplains, middle Odra river, Odonata, oxbow lakes, riparian forests

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