Results 11 to 20 of about 6,424 (109)

Quantum variations of cyclotomic cosets for cyclic stabiliser codes construction

Quantum Information Processing
AbstractCyclotomic 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.
En Chong Yap, Kai Lin Ong
exaly   +5 more sources

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, Cen Jung Tjhai, Marcel Ambroze, Mohammed Ahmed, Mubarak Jibril   +4 more
openaire   +3 more sources

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, Mehrab Najafian, T. Aaron Gulliver   +2 more
openaire   +4 more sources

CYCLOTOMIC COSETS IN THE RING

International Journal of Advanced Research
We consider the ringR_(2p^n q^m )=GF(l)[x]/(x^(2p^n q^m )-1) where p,q,l are distinct odd primes,l is a primitive root both modulo p^n and q^m such that gcd(p^n),(q^m))d.Explicit expressions for all the 2(m n d+m+n+1) Cyclotomic Cosets areobtained, p does not divide q-1 .
openaire   +3 more sources

CYCLOTOMIC COSETS IN THE RING EQUATION

International Journal of Advanced Research
We consider the ringR_(4p^n q^m )=GF(l)[x]/(x^(4p^n q^m )-1) where p,q,l are distinct odd primes,l is a primitive root both modulo p^n and q^m such that gcd (p^n), (q^m)) d.Explicit expressions for all the 4(m n d m n 1) Cyclotomic Cosets areobtained, p does not divide q 1 .
openaire   +3 more sources

Explicit representatives and sizes of cyclotomic cosets and their application to cyclic codes over finite fields

Finite Fields and Their Applications
Cyclotomic 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.
Li Zhu, Jinle Liu, Hongfeng Wu
openaire   +4 more sources

CYCLOTOMIC COSETS MODULO m

JP Journal of Algebra, Number Theory and Applications, 2021
Pinki Devi, Pankaj Kumar
openaire   +3 more sources

On Values of Cyclotomic Polynomials. V [PDF]

, 2003
In this paper, we present three results on cyclotomic polynomials. First, we present results about factorization of cyclotomic polynomials over arbitrary fields K.
Motose, Kaoru, Kaoru Motose
core   +1 more source

Remarks on the Coefficients of Inverse Cyclotomic Polynomials

, 2023
Cyclotomic polynomials play an imporant role in discrete mathematics. Recently, inverse cyclotomic polynomials have been defined and investigated.
Andrica, D., Dorin Andrica, Ovidiu Bagdasar   +2 more
core   +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
doaj   +1 more source