Yazar "Aksoy, Refia" seçeneğine göre listele

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    Öğe
    Cyclic codes over F2 X (F2+vF2) and binary quantum codes
    (University of Nis, 2023) Çalışkan, Fatma; Aksoy, Refia
    In the present study, we define cyclic codes over the commutative principal ideal ring F2 X (F2 + vF2) with v2 = v and obtain some results on cyclic codes over F2 X (F2 + vF2). We also investigate the dual of a cyclic code over F2 X (F2 + vF2) depending on two inner products. We determine a generator polynomial of cyclic codes and give the calculation of the number of cyclic codes over F2 X (F2 + vF2). Furthermore, we show that the Gray images of a cyclic code over F2 X (F2 + vF2) of length n are binary quasi-cyclic codes of length 3n and of index 3. We find numerous binary codes as Gray images of cyclic codes over F2 X (F2 + vF2) and tabulate the optimal ones. Moreover, we show that it is possible to obtain binary quantum error-correcting codes (QECCs) from cyclic codes over F2 X (F2 + vF2).
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    Öğe
    Entanglement-assisted binary quantum codes from skew cyclic codes over F2 x (F2 + vF2)
    (Springer, 2023) Çalışkan, Fatma; Aksoy, Refia; Aydın, Nuh; Liu, Peihan
    In the current paper, we study skew cyclic codes over the ring S := F-2 x (F-2 + vF(2)) with v(2) = v. We investigate the structural properties of skew cyclic codes over the ring S. Also, we describe the dual codes of skew cyclic codes with respect to the Euclidean inner product and the Hermitian inner product. Furthermore, we give a necessary and sufficient condition for a skew cyclic code over S to contain its dual. Using these results, we show that binary quantum error-correcting codes as well as entanglement-assisted quantum error-correcting codes can be constructed from skew cyclic codes over S. Finally, we give examples of binary entanglement-assisted quantum error-correcting codes with good parameters from skew cyclic codes over S.
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    Non-Binary Quantum Codes from Cyclic Codes over Fp x (Fp + vFp)
    (Springer/Plenum Publishers, 2023) Çalışkan, Fatma; Yıldırım, Tülay; Aksoy, Refia
    In this paper, we study cyclic codes over the ring F-p x (F-p + vF(p)), where p is an odd prime and v(2) = v. We first investigate the properties of the ring F-p x (F-p + vF(p)) and the linear codes over this ring. We also define a distance-preserving Gray map from F(p)x(F-p+vF(p)) to F-p(3). We discuss cyclic codes and their dual codes over the ring. Also, we define a set of generators for these codes. As an implementation, we show that quantum error-correcting codes can be obtained from dual containing cyclic codes over the ring by using the CalderbankShor-Steane (CSS) construction. Furthermore, we give some illustrative examples. Finally, we tabulate the non-binary quantum error-correcting codes obtained from cyclic codes over the ring.