Results 21 to 30 of about 11,330 (177)
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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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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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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New binary and ternary LCD codes [PDF]
, 2017 LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3 ...
Galindo, Carlos +3 more
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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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Construction of class fields over cyclotomic fields
, 2015 Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ let $k_\mu$ be the ray class field of $k=\mathbb{Q}(e^{2\pi i/\ell})$ modulo $2p^\mu$. We present certain class fields $K_\mu$ of $k$ such that $k_\mu\leq K_\mu\leq k_{\mu+1}$, and find the ...
Koo, Ja Kyung, Yoon, Dong Sung
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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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Abstract algebra, projective geometry and time encoding of quantum information
, 2005 Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of the integers ...
Planat, Michel R. P., Saniga, Metod
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