Results 1 to 10 of about 10,192,265 (264)
Bounds for Coding Theory over Rings [PDF]
Entropy, 2022 Coding theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. It has been well established that, with the generalization of the algebraic structure to rings, there is
Niklas Gassner +3 more
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On Linear Coding over Finite Rings and Applications to Computing
Entropy, 2017 This paper presents a coding theorem for linear coding over finite rings, in the setting of the Slepian–Wolf source coding problem. This theorem covers corresponding achievability theorems of Elias (IRE Conv. Rec. 1955, 3, 37–46) and Csiszár (IEEE Trans.
Sheng Huang, Mikael Skoglund
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Noncyclic BCH and Srivastava codes over the subgroup of the groups of units of Galois rings $${G}{R}({{q}}^{{u}},{m})$$ for advanced error control [PDF]
Scientific ReportsThis paper presents a systematic algebraic construction of noncyclic generalizations of BCH and Srivastava codes over Galois rings $$GR\left({q}^{u},m\right).$$ The proposed codes are defined via parity-check matrices whose entries are carefully chosen ...
Muhammad Sajjad +4 more
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Frobenius Local Rings of Length 5 and Index of Nilpotency 3
MathematicsThis paper investigates finite local non-chain rings associated by the well-known invariants p,n,m,l, and k, where p is a prime number. In particular, we provide a comprehensive characterization of Frobenius local rings of length l=5 and index of ...
Sami Alabiad, Alhanouf Ali Alhomaidhi
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On Linear Codes over Finite Singleton Local Rings
MathematicsThe study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings.
Sami Alabiad +2 more
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Two New Classes of Codebooks Asymptotically Achieving the Welch Bound
IEEE Access, 2021 Exponential sums over Galois rings have many applications in coding theory, cryptography and algebraic combinatorics. In this article, we employ additive characters and multiplicative characters over Galois rings to present two classes of codebooks, and ...
Shimin Sun, Li Han, Yang Yan, Yao Yao
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On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Mathematics, 2021 In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings.
Ángel Luis Muñoz Castañeda +2 more
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Nonassociative Algebras, Rings and Modules over Them
Mathematics, 2023 The review is devoted to nonassociative algebras, rings and modules over them. The main actual and recent trends in this area are described. Works are reviewed on radicals in nonassociative rings, nonassociative algebras related with skew polynomials ...
Sergey Victor Ludkowski
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Results in Physics, 2021 In this paper, by integrating the phase-cancellation and absorption mechanisms, we proposed and experimentally demonstrated a light-weight coding metamaterial for broadband, wide-angle and polarization-independent radar cross section (RCS) reduction ...
Wei Fang +3 more
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Prime Graph over Cartesian Product over Rings and Its Complement
JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 Graph theory is a branch of algebra that is growing rapidly both in concept and application studies. This graph application can be used in chemistry, transportation, cryptographic problems, coding theory, design communication network, etc.
Farah Maulidya Fatimah +2 more
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