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On Cyclotomic Cosets as Orbit Structures under the Action of Cyclic Subgroups of GL(d,q)

Journal of Advances in Mathematics and Computer Science
Cyclotomic cosets are classical algebraic objects that arise naturally in modular arithmetic, finite field theory, and coding theory, especially in the study of polynomial factorization and cyclic codes. Traditionally, they are defined arithmetically through the formation of sets of the form Ci = {i · pj mod n | j ≥ 0}, and their study has largely ...
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SOME CYCLOTOMIC COSETS IN THE RING R_(8p^n q^m )=GF(l)[x] (x^(8p^n q^m )-1)

International Journal of Advanced Research
We consider the ring R_(8p^n q^m )=GF(l)[x]/(x^(8p^n q^m )-1)where p,q,l are distinct odd primes, l is a primitive root both modulo p^n and q ...
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On reduced expressions for core double cosets

The notion of a reduced expression for a double coset in a Coxeter group was introduced by Williamson, and recent work of Elias and Ko has made this theory more accessible and combinatorial.
Patimo, Leonardo, Ko, Hankyung, Elias, Ben, Libedinsky, Nicolas   +3 more
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Affine and cyclotomic Schur categories

Using the affine web category introduced in a prequel as a building block, we formulate a diagrammatic $\Bbbk$-linear monoidal category, the affine Schur category, for any commutative ring $\Bbbk$.
Wang, Weiqiang, Song, Linliang
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Cyclotomic polynomials

Ciklotomične polinome vpeljemo kot minimalne polinome primitivnih korenov enote nad poljem racionalnih števil. Pokažemo, da imajo celoštevilske koeficiente, ki jih v nadaljevanju obravnavamo bolj podrobno.
Stantič, Klara
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Some arithmetical properties of cyclotomic cosets and their applications

Discrete Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dandan Wang, Xiwang Cao, Jiafu Mi
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Cyclotomic cosets and quantum BCH codes

2010 Sixth International Conference on Natural Computation, 2010
In order to constructing quantum BCH codes from classical BCH codes using CSS constructing method it needs to determine whether the BCH codes contains its dual. Cyclotomic cosets play very important roles in classical error correction theory and quantum error correction theory.
Fangying Xiao, Hanwu Chen
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Cyclotomic cosets and primitive idempotents in semisimple ring

Communications in Algebra, 2019
AbstractLet p1,p2,…,pr,q be distinct primes. Let m=∏i=1rpiαi, where at least two of αi’ s are nonzero positive integers.
Pinki Devi, Pankaj Kumar
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New constructions of Boolean functions using cyclotomic cosets

2016 International Conference on Emerging Trends in Communication Technologies (ETCT), 2016
In this paper, the analysis of cyclotomic coset has been done for construction of Boolean functions. Boolean function used in cryptographic systems should have good cryptographic properties against standard or fast algebraic attacks. The cyclotomic coset plays very important role in cryptography. By using cyclotomic coset leader and minimal polynomial,
Kanchan Verma, Dheeraj Kumar Sharma
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Construction of Strongly Mutually Distinct Sudoku Tables and Solid Sudoku Cubes by Cyclotomic Cosets

IEEE Transactions on Games, 2020
A new method of constructing Sudoku tables (STs) (Sudoku Latin squares) is introduced by making use of individual vectors of cyclotomic cosets of $Z_n$ and their Kronecker product. We show that, it is possible to construct $m$ different STs of order $m$ such that for every $0\leq u, v \leq m-1$ the $(u, v)$ -entry of these $m ...
Mehrab Najafian, Mohammad Hesam Tadayon, Morteza Esmaeili   +2 more
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