Yazar "Dougherty, Steven T." seçeneğine göre listele

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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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    Quasi-Self-Dual Codes over a Non-Unital Ring of Order 4
    (American Mathematical Society, 2023) Dougherty, Steven T.; Sąhinkaya, Serap
    We relate quasi-self-dual codes over a non-unital ring to additive self-dual codes over the additive group of the ring. We show that the Hamming weight enumerator of a quasi-self-dual code over this non-unital ring must belong to the same ring of invariants that self-dual codes over the Frobenius rings with unities belong. Additionally, the Hamming weight enumerator of a Type IV code over E must reside in the same ring of invariants as a Type IV code over the field of order 4. © 2023 American Mathematical Society.
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    Reversible G-codes over the ring Fj,k with applications to DNA codes
    (American Institute of Mathematical Sciences (AIMS), 2023) Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz; Cengellenmis, Yasemin; Dertli, Abdullah; Dougherty, Steven T.
    In this paper, we show that one can construct a G-code from group rings that is reversible. Specifically, we show that given a group with a subgroup of order half the order of the ambient group with an element that is its own inverse outside the subgroup, we can give an ordering of the group elements for which G-codes are reversible of index alpha. Additionally, we introduce a new family of rings, F-j,F-k, whose base is the finite field of order 4 and study reversible G-codes over this family of rings. Moreover, we present some possible applications of reversible G-codes over F-j,F-k to reversible DNA codes. We construct many reversible G-codes over F-4 of which some are optimal. These codes can be used to obtain reversible DNA codes.
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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.