منابع مشابه
NTRU over rings beyond \mathbbZ{\mathbb{Z}}
The NTRU cryptosystem is constructed on the base ring Z. We give suitability conditions on rings to serve as alternate base rings. We present an example of an NTRU-like cryptosystem based on the Eisenstein integers Z[ζ3], which has a denser lattice structure than Z for the same dimension, and which furthermore presents a more difficult lattice problem for lattice attacks, for the same level of ...
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We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over GR(4) are constr...
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Galois rings are regarded as “building blocks” of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently pref...
متن کاملGeneralized Reed-Muller codes over Galois rings
Recently, Bhaintwal and Wasan studied the Generalized Reed-Muller codes over the prime power integer residue ring. In this paper, we give a generalization of these codes to Generalized Reed-Muller codes over Galois rings.
متن کاملSchur rings over a product of Galois rings
The recently developed theory of Schur rings over a finite cyclic group is generalized to Schur rings over a ring R being a product of Galois rings of coprime characteristics. It is proved that if the characteristic of R is odd, then as in the cyclic group case any pure Schur ring over R is the tensor product of a pure cyclotomic ring and Schur rings of rank 2 over non-fields. Moreover, it is s...
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ژورنال
عنوان ژورنال: Applied Mathematics and Nonlinear Sciences
سال: 2020
ISSN: 2444-8656
DOI: 10.2478/amns.2020.2.00041