Yazar "Sahinkaya, Serap" seçeneğine göre listele

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    A note on the graded isoradical of a graded ring
    (Taylor & Francis Inc, 2020) Ilic-Georgijevic, Emil; Sahinkaya, Serap
    We study the graded isoradical of a ring graded by a group. In particular, we compare the graded isoradical and the classical isoradical of a graded ring, examine the question of how the (graded) isoradical of a graded ring depends on the classical isoradical of a ring which corresponds to the identity element of the grading group, and we also give some sufficient conditions under which the classical isoradical of a graded ring is homogeneous. Communicated by Toma Albu
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    G-codes, self-dual G-codes and reversible G-codes over the ring Bj,k
    (Springer, 2021) Dougherty, S. T.; Gildea, Joe; Korban, Adrian; Sahinkaya, Serap
    In this work, we study a new family of rings, B-j,B-k,B- whose base field is the finite field F-pr. We study the structure of this family of rings and show that each member of the family is a commutative Frobenius ring. We define a Gray map for the new family of rings, study Gcodes, self-dual G-codes, and reversible G-codes over this family. In particular, we show that the projection of a G-code over B-j,B-k to a code over B-l,B-m is also a G-code and the image under the Gray map of a self-dual G-code is also a self-dual G-code when the characteristic of the base field is 2. Moreover, we show that the image of a reversible G-code under the Gray map is also a reversible G2(j+k)-code. The Gray images of these codes are shown to have a rich automorphism group which arises from the algebraic structure of the rings and the groups. Finally, we show that quasi- G codes, which are the images of G-codes under the Gray map, are also G(s)-codes for some s.
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    ON CYCLIC AND NEGACYCLIC CODES WITH ONE-DIMENSIONAL HULLS AND THEIR APPLICATIONS
    (Amer Inst Mathematical Sciences-Aims, 2024) Dougherty, Steven T.; Sahinkaya, Serap
    Linear codes over finite fields with small dimensional hulls have received much attention due to their applications in cryptology and quantum computing. In this paper, we study cyclic and negacyclic codes with onedimensional hulls. We determine precisely when cyclic and negacyclic codes over finite fields with one-dimensional hulls exist. We also introduce onedimensional linear complementary pairs of cyclic and negacyclic codes. As an application, we obtain numerous optimal or near optimal cyclic codes with onedimensional hulls over different fields and, by using these codes, we present new entanglement-assisted quantum error-correcting codes (EAQECCs). In particular, some of these EAQEC codes are maximal distance separable (MDS). We also obtain one-dimensional linear complementary pairs of cyclic codes, which are either optimal or near optimal.
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    Self-dual additive codes
    (Springer, 2022) Dougherty, Steven T.; Korban, Adrian; Sahinkaya, Serap
    We define a self-dual code over a finite abelian group in terms of an arbitrary duality on the ambient space. We determine when additive self-dual codes exist over abelian groups for any duality and describe various constructions for these codes. We prove that there must exist self-dual codes under any duality for codes over a finite abelian group Z(pe). They exist for all lengths when p is prime and e is even; all even lengths when p is an odd prime with p = 1 (mod 4) and e is odd with e > 1; and all lengths that are 0 (mod 4) when p is an odd prime with p = 3 (mod 4) and e is odd with e > 1.
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    Skew G-codes
    (World Scientific Publ Co Pte Ltd, 2023) Dougherty, S. T.; Sahinkaya, Serap; Yildiz, Bahattin
    We describe skew G-codes, which are codes that are the ideals in a skew group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. These codes generalize many of the well-known classes of codes such as cyclic, quasicyclic, constacyclic codes, skew cyclic, skew quasicyclic and skew constacyclic codes. Additionally, using the skew G-matrices, we can generalize almost all the known constructions in the literature for self-dual codes.