Murat Güzeltepe

Cyclic codes over some finite quaternion integer rings

In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and decoding algorithm for these codes is given. 2000 AMS Classification: 94B05, 94B15, 94B35, 94B60

Codes over Hurwitz integers

In this study, we obtain new classes of linear codes over Hurwitz integers equipped with a new metric. We refer to the metric as Hurwitz metric. The codes with respect to Hurwitz metric use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither Hamming metric nor Lee metric. Also, we define decoding algorithms for these codes when up to two coordinates of a transmitted code vector are effected by error of arbitrary Hurwitz weight. AMS Classification: 94B05, 94B15, 94B35, 94B60

Quantum Codes From Cyclic Codes Over The Ring R2

Let R 2 denotes the ring F 2 + μF 2 + υ2 + μυF 2 + wF 2 + μwF 2 + υwF 2 + μυwF2. In this study, we construct quantum codes from cyclic codes over the ring R2, for arbitrary length n, with the restrictions μ2 = 0, υ2 = 0, w 2 = 0, μυ = υμ, μw = wμ, υw = wυ and μ (υw) = (μυ) w. Also, we give a necessary and sufficient condition for cyclic codes over R2 that contains its dual. As a final point, we obtain the parameters of quantum error-correcting codes from cyclic codes over R2 and we give an example of quantum error-correcting codes form cyclic codes over R 2.