Yazar "Dougherty, S. T." seçeneğine göre listele

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    Additive complementary dual codes from group characters
    (Institute of Electrical and Electronics Engineers (IEEE), 2022) Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
    Additive codes have become an increasingly important topic in algebraic coding theory due to their applications in quantum error-correction and quantum computing. Linear Complementary Dual (LCD) codes play an important role for improving the security of information against certain attacks. Motivated by these facts, we define additive complementary dual codes (ACD for short) over a finite abelian group in terms of an arbitrary duality on the ambient space and examine their properties. We show that the best minimum weight of ACD codes is always greater than or equal to the best minimum weight of LCD codes of the same size and that this inequality is often strict. We give some matrix constructions for quaternary ACD codes from a given quaternary ACD code and also from a given binary self-orthogonal code. Moreover, we construct an algorithm to determine if a given quaternary additive code is an ACD code with respect to all possible symmetric dualities. We also determine the largest minimum distance of quaternary ACD codes for lengths n <= 10. The obtained codes are either optimal or near optimal according to Bierbrauer et al+. (2009).
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    Additive skew G-codes over finite fields
    (Springer Link, 2023) Dougherty, S. T.; Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
    We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is also an additive skew G-code. Additionally, we propose a matrix construction for additive skew G-codes and use it to construct several examples of extremal self-dual additive skew G-codes over the finite field F4. Such codes have a strong connection to quantum error correcting codes.
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    Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme
    (American Institute of Mathematical Sciences (AIMS), 2022) Dougherty, S. T.; Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
    We present a generator matrix of the form [σ(v1) | σ(v2)], where v1 ϵ RG and v2 ϵ RH, for finite groups G and H of order n for constructing self-dual codes and linear complementary dual codes over the finite Frobenius ring R. In general, many of the constructions to produce self-dual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find self-dual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve 10 of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain 82 new binary linear complementary dual codes, 50 of which are either optimal or near optimal of lengths 41 ≤ n ≤ 61 which are new to the literature.
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    Codes from the Skew Ring ... - ...
    (American Mathematical Society, 2023) Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
    In this work, we study codes generated by elements in the skew group matrix ring M k ( R ) ⋊ φ G M_k(R)\rtimes _{\varphi }G , where R R is a finite commutative Frobenius ring, G G is an arbitrary finite group, and φ \varphi is a group homomorphism from G G to A u t ( M k ( R ) ) Aut(M_k(R)) . We then determine all possible group homomorphisms φ : G → A u t ( M 2 ( F 2 ) ) , \varphi : G \rightarrow Aut(M_2(\mathbb {F}_2)), for the cases where G G is a cyclic group and a dihedral group. Finally, by using skew generator matrices we provide examples of binary self-dual codes and also binary linear optimal codes.
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    Construction of DNA Codes From Composite Matrices and a Bio-Inspired Optimization Algorithm
    (IEEE-INST Electrical Electronics Engineers Inc., 2023) Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz; Dougherty, S. T.
    Indexed keywords SciVal Topics Metrics Funding details Abstract In this work, we present a new construction method for reversible codes. We employ composite matrices derived from group rings and show how to construct these matrices so that they are also reversible. Also in this work, we give an algorithm for calculating conflict free DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, the GC-content constraints with each DNA codeword being free from reverse complement sub-strings. By employing our construction method for reversible codes and our algorithm, we construct a number of DNA codes that satisfy the above constraints. Many of the codes we obtain have better parameters than some known DNA codes and many have parameters that are new to the literature.
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    Dihedral codes with 1-dimensional hulls and 1-dimensional linear complementary pairs of dihedral codes
    (Springer Link, 2023) Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
    In this paper, we study dihedral codes with 1-dimensional hulls and we determine precisely when dihedral codes over fnite felds with 1-dimensional hulls exist. Moreover, we show that these codes come canonically in pairs. We also introduce 1-dimensional linear complementary pairs of dihedral codes and examine the properties of this class of codes. As an application, we obtain 1-dimensional linear complementary pair of dihedral codes, which are either optimal or near optimal.
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    DNA codes from skew dihedral group ring
    (American Institute of Mathematical Sciences (AIMS), 2022) Dougherty, S. T.; Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
    In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing this matrix construction, the ring Fj,k and its associated Gray maps, we show how one can construct reversible codes of length n(2j+k )over the finite field F-4. As an application, we construct a number of DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, and the GC-content constraints with better parameters than some good DNA codes in the literature.
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    Group matrix ring codes and constructions of self-dual codes
    (Springer Link, 2023) Dougherty, S. T.; Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
    In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring M-k(R) and the ring R, where R is the commutative Frobenius ring. We show that codes over the ring M-k(R) are one sided ideals in the group matrix ring M-k(R)G and the corresponding codes over the ring R are G(k)-codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes.
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    A novel method for image encryption using time signature-dependent s-boxes based on latin squares and the playfair system of cryptography
    (Springer Link, 2023) Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
    This paper presents an image encryption algorithm by using time signature-dependent S-Boxes, which are based on Latin squares, the Playfair system of cryptography, and functions that are inspired by the behavior of a Japanese ladder. The encryption algorithm includes four stages: the construction of the S-Box, the generation of keys, image diffusion, and image permutation. The public key is generated from the grey-scale values of the plaintext image and the time signature, and secret key consists of the time signature and two functions from F82 to F82. Permutation and diffusion stages of the encryption algorithm are based on a given S-Box. Moreover, a chaotic map is used in the permutation phase for an effective shuf-fling of pixel positions. The simulation results and security analyses show that the proposed encryption scheme is quite secure and it can resist various cyber attacks effectively.
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    A novel method for image encryption using time signature-dependent s-boxes based on latin squares and the playfair system of cryptography
    (Springer Link, 2024) Dougherty, S. T.; Şahinkaya, Serap; Ü
    This paper presents an image encryption algorithm by using time signature-dependent S-Boxes, which are based on Latin squares, the Playfair system of cryptography, and functions that are inspired by the behavior of a Japanese ladder. The encryption algorithm includes four stages: the construction of the S-Box, the generation of keys, image diffusion, and image permutation. The public key is generated from the grey-scale values of the plaintext image and the time signature, and secret key consists of the time signature and two functions from F82 to F82. Permutation and diffusion stages of the encryption algorithm are based on a given S-Box. Moreover, a chaotic map is used in the permutation phase for an effective shuf-fling of pixel positions. The simulation results and security analyses show that the proposed encryption scheme is quite secure and it can resist various cyber attacks effectively.
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    On additive codes with one-rank hulls
    (Springer Link, 2024) Üstün, Deniz; Şahinkaya, Serap; Dougherty, S. T.
    We study additive codes with 1-rank hulls and examine their properties for various dualities of the finite field of order 4. We give several constructions of additive and linear codes with 1-rank hulls. We also relate these codes to additive complementary dual codes (ACD). We give an interesting non-existence result for additive codes with a 1-rank hull for the duality M2 in terms of the parity of the number of generators. We conclude by giving substantive computations finding codes with one-rank hulls for small lengths using our results.
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    An S-Box construction from exponentiation in finite fields and its application in RGB color image encryption
    (Springer, 2024) Klobusicky, J.; Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
    In this study, the utilization of exponentiation in finite fields is investigated for the purpose of generating pseudo-random sequences which have a crucial role in cryptographic applications. More precisely, a novel method for generating pseudo-random sequences is proposed to construct an initial S-Box which is a key component in various encryption schemes. In addition to that, a shuffling algorithm that leverages the pseudo-random sequences is developed to enhance the effectiveness of the initial S-Box. The utilization of the proposed S-Box is applied to the RGB color images to showcase its performance and robustness in an image encryption scheme.