TATamador Alihia

Tamador Alihia

Qassim University
See Latest Publications
See Most Cited Publications
SciProfiles
Google Scholar

Current Organizations / Institutes

The organizations/institutes from the scholar's latest article

Previous Organizations / Institutes

The organizations / institutes from the scholar's other articles in the past ten years

Tamador Alihia has a total of 23 co-authors. Here are the top co-authors by number of shared publications:

Latest Publications

  • Website
    Google Scholar
    Open Access

    Cyclic Codes over a Commutative Non-Unital Ring

    by Adel Alahmadi, Tamador Alihia, Malak Altaiary, Abdul Nadim Khan, Patrick Solé

    This paper investigates cyclic codes over the commutative non-unital ring I=⟨a,b∣2a=2b=0,a2=b,ab=0⟩, a ring of order four and characteristic two. We develop a structural description of linear and cyclic codes over I, analyze their residue and torsion codes, and characterize self-dual codes. A Gray map from In to F22n is introduced and shown to transform cyclic codes into binary quasi-cyclic codes of index two. Numerical examples for lengths 2≤n≤7 illustrate the diversity of cyclic codes over I and highlight their potential applications.

  • Website
    Google Scholar
    Open Access

    Computational Analysis of Newton-Type Inequalities for Differentiable Strongly Convex Functions via RL-Integrals

    by Ghulam Abbas, Saima Riaz, Tamador Alihia, Khuram Ali Khan, Saba Yasmin, Ramy M. Hafez

    In this paper, new generalizations of Newton-type inequalities for the class of strongly convex functions by utilizing Riemann–Liouville fractional integrals are established. New estimates are obtained for functions that are strongly convex. The established inequalities are further improved. Examples, along with graphs, are provided to demonstrate the validity of the newly established inequalities and comparisons with existing results. It is expected that the results of this paper will open up new avenues of research and may be generalized to other types of fractional operators and generalized convex functions.

    Cited by 2
  • Website
    Google Scholar
    Open Access

    Linear codes over a new commutative non-unital ring of characteristic 2 and order 16: structure, duality, and Gray map

    by Fawziah Alharthi, Tamador Alihia

    We introduce and investigate linear codes over a new finite commutative non-unital ring $ \mathcal{R} = \mathcal{I} + u\,\mathcal{I}, \qquad u^2 = 0, $ where $ \mathcal{I} = \langle a,b \mid 2a = 2b = 0,\ a^2 = b,\ ab = 0 \rangle. $ The ring $ \mathcal{R} $ has characteristic $ 2 $, order $ 16 $, and a rich nilpotent structure, providing a new algebraic setting for coding theory beyond finite fields and Frobenius rings. We establish a comprehensive framework for linear codes over $ \mathcal{R} $ by describing the module structure of $ \mathcal{R} $ over $ \mathbb{F}_2 + u\mathbb{F}_2 $ and introducing residue and torsion codes. Using this residue-torsion framework, we derive characterizations of self-orthogonal, quasi-self-dual, self-dual, and free codes together with explicit descriptions of their duals. Furthermore, we construct an $ \mathbb{F}_2+u\mathbb{F}_2 $-linear Gray map and prove that it is a Lee-weight-preserving isometry from $ \mathcal{R}^n $ to $ (\mathbb{F}_2+u\mathbb{F}_2)^{2n} $. We also develop the theory of Hamming and Lee weights, establish the corresponding weight enumerators, and investigate their structural properties. Finally, several explicit examples are constructed and verified using the computational algebra system MAGMA, illustrating the existence of quasi-self-dual, self-dual, and Type Ⅳ codes together with their weight distributions. These results demonstrate that the ring $ \mathcal{R} $ provides a natural and effective framework for constructing and studying new families of linear codes over finite non-unital rings, thereby enriching the algebraic foundations of coding theory.

  • Website
    Google Scholar
    Open Access

    Analysis of Newton-type inequalities for differentiable hyperbolic $ p $-convex functions via RL-integrals

    by Saima Riaz, Khuram Ali Khan, Tamador Alihia, Ghulam Abbas, Tahreem Akram

    In this paper, new generalizations of Newton-type inequalities for the class of hyperbolic $ p $-convex functions by utilizing Riemann-Liouville fractional integrals are established. By means of an auxiliary identity connected with the Riemann-Liouville fractional integrals, new estimates are obtained for functions that are hyperbolic $ p $-convex. The established inequalities are further improved by the effective use of Hölder's inequality and the power-mean inequality. Examples along with graphs are provided to demonstrate the validity of the newly established inequalities and comparisons with existing results. The results of this paper will open up new avenues of research and may be generalized to other types of fractional operators and generalized convex functions.

  • Website
    Google Scholar
    Open Access

    Analysis of inclusions using $ s $-type convex interval-valued functions via Riemann-Liouville fractional integrals

    by Ammara Nosheen, Khuram Ali Khan, Mariam Aslam, Atiq Ur Rehman, Tamador Alihia, Salwa El-Morsy

    This paper examines a family of convex interval-valued (IVC) functions using the Riemann-Liouville (RL) integrals. Hermite-Hadamard (HH) and Hermite-Hadamard-Fejér (HHF) type inclusions are developed by employing the $ s $-type convexity of interval-valued (Ⅳ) functions. Some inclusions for the product of $ s $-type (IVC) functions are also established involving RL integrals. All main results are furthur refined into inclusions and inequalities for $ s $-type IVC functions and $ s $-type convex point-valued functions, respectively, involving the ordinary integral. In addition, several consequences of the primary results are explored demonstrating the connections between point-valued convex functions, IVC functions, and $ s $-type IVC functions. Each key conclusion is validated numerically. The results of this paper might open the path for new avenues in modeling, optimization problems, interval differential equations, and fuzzy Ⅳ functions that involve both discrete and continuous variables simultaneously.

    Cited by 1
  • Website
    Google Scholar
    Open Access

    On the Duality of Codes over Non-Unital Commutative Ring of Order p2

    by Tamador Alihia

    This paper establishes an extended theoretical framework centered on the duality of codes constructed over a special class of non-unital, commutative, local rings of order p2, where p is a prime satisfying p≡1mod4 or p≡3mod4. The work expands the traditional scope of coding theory by developing and adapting a generalized recursive approach to produce quasi-self-dual and self-dual codes within this algebraic setting. While the method for code generation is rooted in the classical build-up technique, the primary focus is on the duality properties of the resulting codes—especially how these properties manifest under different congruence conditions on p. Computational examples are provided to illustrate the effectiveness of the proposed methods.

    Cited by 1
  • Website
    Google Scholar
    Open Access

    Analysis of solvability and representation of general solutions for anti-Hermitian constrained quaternion matrix equations

    by Abdur Rehman, Ivan Kyrchei, Khuram Ali Khan, Tamador Alihia, Salwa El-Morsy

    This paper addresses the constrained system of quaternion matrix equations incorporating anti-Hermitian properties, driven by the significance of symmetric solutions in diverse applications. Solvability conditions are determined via rank equalities and relationships derived from Moore–Penrose inverses and induced projectors. Explicit solution representations are obtained, utilizing the Moore–Penrose inverse and projections. The originality of the results is established through a novel technique based on quaternion row-column determinant theory, supported by a numerical validation. This approach retains its innovative character even when extended to complex matrix equations using conventional determinants.

  • Website
    Google Scholar
    Open Access

    Integral inequalities involving a new class of generalized strongly modified $ (p, h) $-convex functions

    by Mudassir Hussain Bukhari, Ammara Nosheen, Khuram Ali Khan, Salwa El-Morsy, Tamador Alihia

    A novel class of generalized strongly modified (GSM) $ (p, h) $-convex functions (CFs) was presented in paper and its fundamental properties were established. Schur, Hermite-Hadamard (H-H), and Fejér inequalities were proved for this new notion of convexity. Several illustrations have been incorporated by selecting several GSM $ (p, h) $-CFs to substantiate the existence and feasibility of Schur, H-H, and Fejér-type inequalities. These inequalities are valuable resources for analyzing the characteristics of newly defined GSM $ (p, h) $-CFs. A comparison was given to show that the results of this study represent a significant improvement over those of earlier publications.

    Cited by 4
  • Website
    Google Scholar
    Open Access

    The Build-Up Construction for Codes over a Commutative Non-Unitary Ring of Order 9

    by Adel Alahmadi, Tamador Alihia, Rowena Alma Betty, Lucky Galvez, Patrick Solé

    The build-up method is a powerful class of propagation rules that generate self-dual codes over finite fields and unitary rings. Recently, it was extended to non-unitary rings of order 4, to generate quasi self-dual codes. In the present paper, we introduce three such propagation rules to generate self-orthogonal, self-dual and quasi self-dual codes over a special non-unitary ring of order 9. As an application, we classify the three categories of codes completely in length at most 3, and partially in lengths 4 and 5, up to monomial equivalence.

    Cited by 6