Results 51 to 60 of about 12,236 (229)

Good Integers: A Structural Review With Applications to Polynomial Factorization and Algebraic Coding Theory

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
For nonzero coprime integers a and b, a positive integer l is said to be good with respect to a and b if there exists a positive integer k such that l divides ak + bk. Since the early 1990s, the notion of good integers has attracted considerable attention from researchers. This continued interest stems from both their elegant number‐theoretic structure
Somphong Jitman, Anwar Saleh Alwardi
wiley   +1 more source

PROPERTIES OF GROUPS G OF DOUBLE ERRORS AND ITS INVARIANTS IN BCH CODES

Системный анализ и прикладная информатика, 2018
The goal of the work is the further extending the scope of application of code automorthism in methods and algorithms of error correction by these codes. The effectiveness of such approach was demonstrated by norm of syndrome theory that was developed by
V. A. Lipnitskij, A. V. Serada
doaj   +1 more source

Self-dual cyclic codes over finite chain rings [PDF]

, 2014
Let $R$ be a finite commutative chain ring with unique maximal ideal $\langle \gamma\rangle$, and let $n$ be a positive integer coprime with the characteristic of $R/\langle \gamma\rangle$. In this paper, the algebraic structure of cyclic codes of length
Chen, Bocong, Ling, San, Zhang, Guanghui
core  

The cyclotomic polynomial topologically [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2012
Abstract. We interpret the coefficients of the cyclotomic polynomial in terms of simplicial homology.
Musiker, Gregg, Reiner, Victor
openaire   +2 more sources

Chebotarev's theorem for cyclic groups of order pq$pq$ and an uncertainty principle

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3841-3856, December 2025.
Abstract Let p$p$ be a prime number and ζp$\zeta _p$ a primitive p$p$th root of unity. Chebotarev's theorem states that every square submatrix of the p×p$p \times p$ matrix (ζpij)i,j=0p−1$(\zeta _p^{ij})_{i,j=0}^{p-1}$ is nonsingular. In this paper, we prove the same for principal submatrices of (ζnij)i,j=0n−1$(\zeta _n^{ij})_{i,j=0}^{n-1}$, when n=pr ...
Maria Loukaki
wiley   +1 more source

q-Analogue of a binomial coefficient congruence

International Journal of Mathematics and Mathematical Sciences, 1995
We establish a q-analogue of the congruence (papb)≡(ab)   (modp2) where p is a prime and a and b are positive integers.
W. Edwin Clark
doaj   +1 more source

General Gate Teleportation and the Inner Structure of Its Clifford Hierarchies

Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 15985-15997, 30 November 2025.
ABSTRACT The quantum gate teleportation mechanism allows for the fault‐tolerant implementation of “Clifford hierarchies” of gates assuming, among other things, a fault‐tolerant implementation of the Pauli gates. We discuss how this method can be extended to assume the fault‐tolerant implementation of any orthogonal unitary basis of operators, in such a
Samuel González‐Castillo, Elías F. Combarro, Ignacio F. Rúa, José Ranilla   +3 more
wiley   +1 more source

A Note on Factorization and the Number of Irreducible Factors of xⁿ − λ over Finite Fields

Mathematics
Let 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
doaj   +1 more source

Growth problems in diagram categories

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3454-3469, November 2025.
Abstract In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
Jonathan Gruber, Daniel Tubbenhauer
wiley   +1 more source

Unitary cyclotomic polynomials

, 2019
The notion of block divisibility naturally leads one to introduce unitary cyclotomic polynomials. We formulate some basic properties of unitary cyclotomic polynomials and study how they are connected with cyclotomic, inclusion-exclusion and Kronecker polynomials.
Moree, Pieter, Tóth, László
openaire   +4 more sources