Judul: Konstruksi Kode Linear Biner Optimal Kuat Berdimensi 5 dan 7
Abstrak: Kode diciptakan untuk mendeteksi atau mengoreksi galat (error) akibat saluran terganggu. Dalam hal ini sebelum dikirim , semua pesan akan diubah menjadi kata kode (codeword) dengan cara menambahkan beberapa simbol ekstra pada simbol pesan. Proses pengubahan pesan menjadi kata kode disebut enkoding. Perangkat yang mengubah pesan menjadi kata kode disebut enkoder. Kode merupakan himpunan kata kode. Pendefinisian kode ini dilakukan sedemikian sehingga apabila terjadi perubahan beberapa simbol pada kata kode, maka galat itu bisa dipulihkan oleh dekoder. Dekoder merupakan perangkat yang mengubah barisan s ang diterima menjadi kata kode. Kata kode tersebut dipulihkan menjadi pesan asli. imbol y Suatu kode 􀜥 􀙃 􀥲􀬶 􀯡 subruang dari ruang vektor 􀥲􀬶 􀯡 disebut kode linear biner. Jika kode C dengan panjang n, dimensi k dan jarak minimum d maka disebut kode [n, k, d]. Masalah utama di dalam aljabar teori koding adalah mengoptimalkan salah satu parameter n, k, dan d ketika dua nilai yang lain telah ditentukan. Masalah tersebut mengarah pada pendefinisian fungsi D ( n, k ) = maks { d / kode [ n, k, d ] ada } untuk optimal-D K ( n, d ) = maks { k / kode [ n, k, d ] ada } untuk optimal-K N ( k, d ) = min { n / kode [ n, k, d ] ada } untuk optimal-N Dalam hal ini, suatu kode C dengan parameter [ n, k, d ] disebut optimal-D (optimal jarak minimum), jika C ada (telah berhasil dikonstruksi) dan telah pula dibuktikan bahwa tidak ada kode dengan parameter [ n, k, d + 1]. Jika kode linear [n, k, d] ada dan telah berhasil dibuktikan bahwa kode linear [n-1, k, d] tidak ada maka kode disebut optimal-N. Selanjutnya jika kode linear [n, k, d] ada dan telah berhasil dibuktikan bahwa kode linear [n, k+1, d] tidak ada, maka kode tersebut disebut optimal –K. Kode linear C dengan parameter [n, k, d] disebut kode optimal kuat jika kode [n, k, d] ada dan telah dibuktikan bahwa kode [n+1, k+1, d] tidak ada. Pada penelitian ini akan dikonstruksi kode-kode optimal kuat berjarak minimum 5 dan 7 berdasarkan teorema Gilbert-Varshamov bound dan pengembangan metode komputasi dengan software MAPLE. Dalam hal ini dikonstruksi kode dasar [n, k, d], selanjutnya dari kode dasar ini dikonstruksi tahap demi tahap kode [n+1, k+1,d], [n+2, k+2, d],…dan seterusnya sampai diperoleh kode C dengan parameter [􀝊􁇱, 􀝇􁇱, 􀝀􁈿 yang tidak bisa diperluas lagi dan telah diketahui dari hasil penelitian sebelumnya kode dengan parameter [􀝊􁇱 􀵅 1, 􀝇􁇱 􀵅 1, 􀝀􁈿 tidak ada. (informasi terkini eksistensi suatu kode berdasarkan tabel Brouwer terbarukan secara online). Hasil konstruksi kode C [􀝊􁇱, 􀝇􁇱, 􀝀􁈿 ini yang disebut kode optimal kuat. Kode C dapat digunakan sebagai kode dasar untuk diperluas menjadi kode optimal kuat berikutnya.
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Judul: Konstruksi Kode Linear Biner Optimal Kuat Berjarak Minimum 13 Dan 15
Abstrak: A linear binary code of length n over is defined as subspace of . A code has three parameters that attached to it, namely length, dimension, and minimum distance. A code with length n, dimension k and minimum distance d is often called [n, k, d]-code. The main problem in algebra coding theory is optimizing one of parameters n, k and d. Given two that others were known. Based on Gilbert-Varshamov bound, if a [n, k, d]-code is exist and the code can not be expanded, we call it strongly optimal code. In this thesis, we construct strongly optimal code with minimum distance of 13 and 15. In constructing the code, we created a theorem and algorithm based on Gilbert-Varshamov bound, then we implement the algorithm to MAPLE programming language. Because of computational limitations, the program can only construct up to k = 9 for d = 13 and d = 15.
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Judul: Phylogeography and Species Limits in the Papuan White Snake (Micropechis ikaheka) (Reptilia: Serpentes: Elapidae)
Abstrak: Papua white snake, Micropechis ikaheka, has been distingushed into two subspecies M.i. ikaheka and M.i. fasciatus. However, due to lack of data on their morphology, distribution and ecology, both subspecies often ignored in scintific discussions and refers only byas , Micropechis ikaheka. This study was designed to document the differences between M.i. ikaheka and M.i fasciatus by using scales characteristics and reproductive organ or hemipenes. The study also examine, zoogeography, habitat, diet and cannibalism of both subspecies to better understanding the the ecology of one of the most venomous snakes in the world. This study consists of three topics with method and also different in the size samples, respectively. The first study is the histology and microtopography of the skin were studied using paraffin method and Scanning Electron Microscope (SEM). The second is the hemipenis were examined by following Myers and Cadle (2003), and Zaher and Prudente (2003). The third is the abdominal surgery was carried out to document diet type and the investigate phenomenon of cannibalism in the snake. Specimens for this study came from the collection from Museum Zoologicum Bogoriense (MZB) and Universitas Negeri Papua’s Laboratory (LZU). The research result also indicated that the markers of skin and hemipenis described the same structure and microornamentation in all M. ikaheka groups being compared. Based specimens examined morphological descriptions do not s support the further differentiation in Micropechis. In short, two markers that used in this study could not sufficiently indicate the differences in the level of species and subspecies of M. ikaheka. The study, however, were able to delineate zoogeography and skin color patterns, which fall into four groups: M. i. ikaheka; M. i. fasciatus. M. i. ssp. “intermediate”; and M. i. ssp “black”. This study also revealed that color variations did not overlap in their geographic distribution. It is therefore, it suggested that environmental factors may contribute to the skin color variations. It also assumed that habitat discontinuous and biogeography factors may also cause the loss of the connection between the original populations (vicarians) or follow colonization events (dispersal). The examined of 22 stomach contents of M. ikaheka shows this species is carnivorous, and prey on vertebrates such as amphibians, fish, reptiles, and Mammals. These snakes are opportunistic predators since they prey on all that can be captured, but mainly reptiles (61.5%), followed by mammals and fish (both 15.4%), and amphibians (7.7%). Although categorized as terrestrial animal, the diet study showed that M. ikaheka snakes often go into the water to hunt for fish (the sample from Yapen island), including eel (the sample from Aru island). Based on prey items indentified, there is evidence that M. ikaheka is cannibal. At this time, there still no record on reason for cannibalism, but it is assumed that cannibalism was due to competition between populations and means to control population.
Keyword: geographic variation, white snake, papua