Results 1 to 10 of about 1,812,540 (189)
Construction of Some New Quantum BCH Codes
IEEE Access, 2018 Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have been studied extensively. One can construct quantum stabilizer codes with good parameters using classical BCH codes. In this paper, our goal is to find such classical BCH codes.
Ming Zhang +3 more
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On the subfields of cyclotomic function fields [PDF]
Czechoslovak Mathematical Journal, 2013 Let \(K={\mathbb F}_q(T)\) be the rational function field over the finite field with \(q\) elements, where \(q\) ia a power of an odd prime. Let \(P\) be a monic irreducible polynomial in \({\mathcal O}_K={\mathbb F}_q[T]\) of degree \(d>0\), \(K_P=K(\lambda _P)\) be the cyclotomic function field where \(\Lambda _P\) is the set of \(P\)-torsion ...
Zhao, Zhengjun, Wu, Xia
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Forum of Mathematics, Sigma, 2018 We introduce a path theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher-level generalizations over fields of arbitrary characteristic.
C. BOWMAN, A. G. COX
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Representation of cyclotomic fields and their subfields [PDF]
Indian Journal of Pure and Applied Mathematics, 2013 Let $\K$ be a finite extension of a characteristic zero field $\F$. We say that the pair of $n\times n$ matrices $(A,B)$ over $\F$ represents $\K$ if $\K \cong \F[A]/< B >$ where $\F[A]$ denotes the smallest subalgebra of $M_n(\F)$ containing $A$ and $< B >$ is an ideal in $\F[A]$ generated by $B$.
Reddy, A. Satyanarayana +2 more
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ITM Web of Conferences, 2017 We investigate three classes of Ding-Helleseth-generalized cyclotomic sequences of length pq. We derive the linear complexity and the minimal polynomial of above-mentioned sequences over the finite fields of orders p and q, where p and q are two odd ...
Edemskiy Vladimir, Sokolovskiy Nikita
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A Construction of Rotated Lattices via Totally Real Subfields of the Cyclotomic Field Q(z_p)
Trends in Computational and Applied Mathematics, 2019 The theory of lattices have shown to be useful in information theory and rotated lattices with high modulations diversity have been extensively studied as an alternative approach for transmission over a Rayleigh-fading channel, where the performance of ...
Antonio A. Andrade +2 more
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About Some Split Central Simple Algebras
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 In this paper we study certain quaternion algebras and symbol algebras which split.
Savin Diana
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Extended Genus Fields of Abelian Extensions of Rational Function Fields
AxiomsIn this paper, we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. For the general case, we use the fact that the extended genus fields
Juan Carlos Hernandez-Bocanegra +1 more
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Rotated Z^n-Lattices via Real Subfields of Q(\zeta_2r)
Trends in Computational and Applied Mathematics, 2019 A method for constructing rotated Z^n-lattices, with n a power of 2, based on totally real subfields of the cyclotomic field Q(\zeta_{2^r}), where r\geq 4 is an integer, is presented. Lattices exhibiting full diversity in some dimensions n not previously
Antonio A. Andrade, José C. Interlando
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A Note on Factorization and the Number of Irreducible Factors of xn − λ over Finite Fields
MathematicsLet Fq be a finite field, and let n be a positive integer such that gcd(q,n)=1. The irreducible factors of xn−1 and xn−λ are fundamental concepts with wide applications in cyclic codes and constacyclic codes.
Jinle Liu, Hongfeng Wu
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