Results 11 to 20 of about 2,328 (103)
Cyclotomic Cosets, the Mattson–Solomon Polynomial, Idempotents and Cyclic Codes [PDF]
Signals and Communication Technology, 2017 La importante familia de códigos cíclicos binarios se explora en este capítulo. Comenzando con los cosets ciclotómicos, se introducen los polinomios mínimos. Se describe el polinomio de Mattson–Solomon y se demuestra que es una transformada de Fourier discreta inversa basada en una raíz primitiva de la unidad.
Martin Tomlinson +4 more
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D-Optimal Designs: A Mathematical Programming Approach Using Cyclotomic Cosets [PDF]
Informatica, 2011 In this paper, a novel approach involving the concepts from mathematical programming and number theory is proposed to find the D-optimal designs. In specific, we will propose a mathematical formulation for the D-optimal design. In addition to that, we will present the use of cyclotomic cosets in the mathematical formulation, in order to reduce the ...
Mujahid N. Syed +2 more
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Structured quasi‐cyclic low‐density parity‐check codes based on cyclotomic cosets
IET Communications, 2015 This study considers the construction of four‐cycle free quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes. These codes are based on the cyclotomic cosets of q modulo n where q is a prime power,
Morteza Esmaeili +2 more
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Quantum variations of cyclotomic cosets for cyclic stabiliser codes construction
Quantum Information ProcessingAbstractCyclotomic cosets are intrinsically linked with the design and construction of classical cyclic codes whose properties can be inferred from the coset structures. This paper proposes some new quantum variations of cyclotomic cosets for cyclic stabiliser construction.
Yap, En Chong, Ong, Kai Lin
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Finite Fields and Their ApplicationsCyclotomic coset is a classical notion in the theory of finite field which has wide applications in various computation problems. Let $q$ be a prime power, and $n$ be a positive integer coprime to $q$. In this paper we determine explicitly the representatives and the sizes of all $q$-cyclotomic cosets modulo $n$ in the general settings.
Zhu, Li, Liu, Jinle, Wu, Hongfeng
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Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture
Proceedings of the London Mathematical Society, Volume 127, Issue 5, Page 1268-1337, November 2023., 2023 Abstract We offer some theorems, mainly finiteness results, for certain patterns in elliptical billiards, related to periodic trajectories; these seem to be the first finiteness results in this context. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in (0,π)$(0,\pi )$, there are only finitely many ...
Pietro Corvaja, Umberto Zannier
wiley +1 more source
Categorification of integral group rings extended by one dimension
Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1617-1641, October 2023., 2023 Abstract The integral group rings ZG$\mathbb {Z}G$ for finite groups G$G$ are precisely those fusion rings whose basis elements have Frobenius–Perron dimension 1, and each is categorifiable in the sense that it arises as the Grothendieck ring of a fusion category.
Andrew Schopieray
wiley +1 more source
Quasi-Cyclic Codes Via Unfolded Cyclic Codes and Their Reversibility
IEEE Access, 2019 The finite field $\mathbb {F}_{q^\ell }$ of $q^\ell $ elements contains $\mathbb {F}_{q}$ as a subfield. If $\theta \in \mathbb {F}_{q^\ell }$ is of degree $\ell $ over $\mathbb {F}_{q}$ , it can be used to unfold elements of $\mathbb {F}_{q^\
Ramy Taki Eldin, Hajime Matsui
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Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes
IEEE Access, 2019 Although quantum maximal-distance-separable (MDS) codes that satisfy the quantum singleton bound have become an important research topic in the quantum coding theory, it is not an easy task to search for quantum MDS codes with the minimum distance that ...
Jianzhang Chen +4 more
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Applications of Constacyclic Codes to Some New Entanglement-Assisted Quantum MDS Codes
IEEE Access, 2019 Generally, it is not easy to construct quantum maximal-distance-separable (MDS) codes with the minimum distance greater than $\frac {q}{2}+1$ . The minimum distance of quantum MDS codes can achieve $\frac {q}{2}+1$ or exceed $\frac {q}{2}+1$ by ...
Jianzhang Chen +5 more
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