Weight Distribution dari Kode atas Galois Ring GR(2^3) Menggunakan Lee Distance
Keywords:
Galois ring, kode linear, lee distance, deteksi eror, koreksi erorAbstract
Penelitian ini bertujuan untuk menganalisis konstruksi dan performa kode linear yang dibangun pada Galois ring menggunakan metrik Lee distance dalam menentukan kemampuan deteksi dan koreksi eror. Metode penelitian yang digunakan adalah kajian pustaka melalui studi literatur terhadap berbagai referensi relevan mengenai teori kode linear, Galois ring, dan penerapan Lee distance. Kode linear dibentuk sebagai submodul berdimensi dua dengan panjang kode , menggunakan dua pasangan vektor generator bebas linear yang berbeda, yaitu , untuk matriks generator , dan , untuk matriks generator . Setiap kombinasi linear dari kedua generator menghasilkan 64 codeword, yang kemudian dihitung bobot Lee-nya untuk menentukan distribusi bobot dan jarak minimum kode. Hasil penelitian menunjukkan bahwa submodul pertama memiliki bobot minimum dengan jarak minimum , sehingga mampu mendeteksi satu eror namun belum dapat mengoreksi eror. Sementara itu, submodul kedua memiliki bobot minimum dengan jarak minimum , sehingga mampu mendeteksi dua eror dan mengoreksi satu eror. Hasil ini menunjukkan bahwa pemilihan vektor generator berpengaruh terhadap peningkatan kemampuan deteksi dan koreksi eror pada kode linear yang dikonstruksi atas .
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