Membangun Kode Golay (24, 12, 8) Dengan Matriks Generator Dan Menggunakan Aturan Kontruksi

The binary (24, 12, 8) extended Golay code can be constructed through the direct sum operation with involve two product codes. This method form the generator matrix framework of the (24, 12, 8) Golay code that is based on the so-called Turyn or |a + x|b + x|a + b + x| construction, where a,b C1 and x C. C1 and C is the (8, 4, 4) linear block codes. C can be gotten by applying construction rules to get the generator matrix of C. With C1 and C and by applying the generator matrix framework of the (24. 12, 8) Golay code get the binary (24, 12, 8) extended Golay code

Menentukan Invers Drazin Dari Matriks Singular

A singular matrix A with size has a inverse be called Drazin inverse and denoted by . This inverse can be obtained by specifying a generalized Modal matrix and Jordan canonical form of matrix A. Generalized Modal matrix is a matrix where its columns consisting of generalized eigen vectors from the matrix A, while the Jordan canonical form is a matrix which entries on its main diagonal consisting of Jordan block matrix . Next, two matrices were used to determine Drazin inverse of matrix A

Automorfisma Graf Warna Cayley Yang Dibangun Oleh Suatu Grupoid

Groupoid adalah suatu himpunan tak kosong yang tertutup terhadap operasi biner, himpunan generator grupoid merupakan subset dari grupoid dimana setiap elemen grupoid dapat ditulis sebagai hasilkali berhingga pada elemen generator.Graph warna Cayley digraph dengan titik-titiknya adalah dan himpunan busurnya . Generator grupoid befungsi sebagai warna dan arah busur digraph.Pemetaan adalah pemetaan bijektif antara graph dengan dirinya sendiri.. Automorphism parsial pada graph warna Cayley adalah pemetaan bijektif antara dua tail graph warna Cayley . Himpunan Automorphisma Parsial graph warna Cayley adala

Membangun Kode Golay (24, 12, 8) Dengan Matrtks Generator Dan Menggunakan Kriteria Permutasi

- -One of the more useful block codes k the binary Q4, .12, 8) etended Golay code.The binary (24, 12, 8) actended Golay code can be constructed through the direct sum operationwith irwolvetwo product codes. This methodform the generator matrixframework of the (24, 12, 8) Golay code that isbasedontheso-calledTuytnorla+xlb +xla+ b+xlcanstntction,wherea,bE Crandxe C', C,andC',is the (8, 4, 4) Iinear block codes. C, can be gotten through row permutation of the parity submaffix of CLWith q and C', and by applying the generator matrixframework of the (24. 12, S) Golry code get the binary(24, 12, 8) utended Golay code..Keyword :Block codes, direct sum, Goloy Code, product codes