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CODES OVER THE MULTIPLICATIVE HYPERRINGS
(Turkic World Mathematical Soc, 2021) Akbiyik, Seda Yamac
Codes over hyperstructures have more codewords than codes over rings(or fields). It implies that they have higher rate than codes over rings (or fields). So, in this paper the codes over multiplicative hyperrings are studied. Linear codes and the cyclic codes over multiplicative hyperrings are constructed.
Determinants of circulant matrices with Gaussian Nickel Fibonacci numbers
(Univ Nis, Fac Sci Math, 2023) Yilmaz, Fatih; Ertas, Aybuke; Akbiyik, Seda Yamac
In this study, we consider 7Cn := circ (GN1, GN2, ... , GNn) circulant matrices whose entries are the Gaussian Nickel Fibonacci numbers GN1, GN2, ... , GNn. Then, we compute determinants of 7Cn by exploiting Chebyshev polynomials of the second kind. Moreover, we obtain Cassini's identity and the D'Ocagne identity for the Gaussian Nickel Fibonacci numbers.
De Moivre-type identities for the Jacobsthal numbers
(Bulgarian Acad Science, 2021) Akbiyik, Mucahit; Akbiyik, Seda Yamac
The main aim of this study is to obtain De Moivre-type identities for Jacobsthal numbers. Also, this paper presents a method for constructing the second order Jacobsthal and Jacobsthal third-order numbers and the third-order Jacobsthal and Jacobsthal-Lucas numbers. Moreover, we give some interesting identities, such as Binet's formulas for some specific third-order Jacobsthal numbers that we derive from De Moivre-type identities.