DUAL CODE AND MACWILLIAMS IDENTITY ON ADDITIVE CODE

Additive code is a generalization of linear code. It is defined as subgroup of a finite Abelian group. The definitions of Hamming distance, Hamming weight, weight distribution, and homogeneous weight distribution in additive code are similar with the definitions in linear code. Different with linear code where the dual code is defined using inner product, additive code using theories in group to define its dual code because in group theory we do not have term of inner product. So, by this thesis, the definitions of dual code in additive code will be discussed. Then, this thesis discuss about a familiar theorem in dual code theory, that is MacWilliams Identity. Next, this thesis discuss about how to proof of MacWilliams Identity on adiitive code using dual codes which are defined.

Studi Perbandingan Algoritma Pencarian String dalam Metode Approximate String Matching untuk Identifikasi Kesalahan Pengetikan Teks

Error typing resulting in the change of standard words into non-standard words are often caused by misspelling. This can be addressed by developing a system to identify errors in typing. Approximate string matching is one method that is widely implemented to identify error typing by using several string search algorithms, i.e. Levenshtein Distance, Hamming Distance, Damerau Levenshtein Distance and Jaro Winkler Distance. However, there is no study that compares the performance of the four algorithms. Therefore, this research aims to compare the performance between the four algorithms in order to identify which algorithm is the most accurate and precise in the search string based on various errors typing. Evaluation is performed by using users’ relevance judgments which produce the mean average precision (MAP) to determine the best algorithm. The result shows that Jaro Winkler Distance algorithm is the best in word-checking with 0.87 of MAP value when identifying the typing error of 50 incorrect words.Keywords: Errors typing, Levenshtein, Hamming, Damerau Levenshtein, Jaro Winkler Abstrak. Kesalahan pengetikan mengakibatkan kata baku berubah menjadi kata tidak baku karena ejaan yang digunakan tidak sesuai. Hal tersebut dapat ditangani dengan mengembangkan sistem untuk mengidentifikasi kesalahan pengetikan. Metode approximate string matching merupakan salah satu metode yang banyak diterapkan untuk mengidentifikasi kesalahan pengetikan dengan berbagai jenis algoritma pencarian string yaitu Levenshtein Distance, Hamming Distance, Damerau Levenshtein Distance dan Jaro Winkler Distance. Akan tetapi studi perbandingan kinerja dari keempat algoritma tersebut untuk Bahasa Indonesia belum pernah dilakukan. Oleh karena itu penelitian ini bertujuan untuk melakukan studi perbandingan kinerja dari keempat algoritma tersebut sehingga dapat diketahui algoritma mana yang lebih akurat dan tepat dalam pencarian string berdasarkan kesalahan penulisan yang bervariasi. Evaluasi yang dilakukan menggunakan user relevance judgement yang menghasilkan nilai mean average precision (MAP) untuk menentukan algoritma yang terbaik. Hasil penelitian terhadap 50 kata salah menunjukkan bahwa algoritma Jaro Winkler Distance terbaik dalam melakukan pengecekan kata dengan nilai MAP sebesar 0,87.Kata Kunci: Kesalahan pengetikan, Levenshtein, Hamming, Damerau Levenshtein, Jaro Winkler