منابع مشابه
Generalized twisted centralizer codes
An important code of length n is obtained by taking centralizer of a square matrix over a finite field Fq. Twisted centralizer codes, twisted by an element a ∈ Fq, are also similar type of codes but different in nature. The main results were embedded on dimension and minimum distance. In this paper, we have defined a new family of twisted centralizer codes namely generalized twisted centralizer...
متن کاملTwisted Centralizer Codes
Given an n× n matrix A over a field F and a scalar a ∈ F , we consider the linear codes C(A, a) := {B ∈ F | AB = aBA} of length n2. We call C(A, a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a = 1) is at most n, howe...
متن کاملOn the dimension of twisted centralizer codes
Given a field F , a scalar λ ∈ F and a matrix A ∈ F, the twisted centralizer code CF (A, λ) := {B ∈ F | AB − λBA = 0} is a linear code of length n. When A is cyclic and λ 6= 0 we prove that dimCF (A, λ) = deg(gcd(cA(t), λcA(λt))) where cA(t) denotes the characteristic polynomial of A. We also show how CF (A, λ) decomposes, and we estimate the probability that CF (A, λ) is nonzero when |F | is f...
متن کاملCentralizer Construction for Twisted Yangians
For each of the classical Lie algebras g(n) = o(2n+ 1), sp(2n), o(2n) of type B, C, D we consider the centralizer of the subalgebra g(n−m) in the universal enveloping algebra U(g(n)). We show that the nth centralizer algebra can be naturally projected onto the (n− 1)th one, so that one can form the projective limit of the centralizer algebras as n → ∞ with m fixed. The main result of the paper ...
متن کاملA generalization of quasi-twisted codes: Multi-twisted codes
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this work we introduce a new generalization of QT codes that we call multi-twisted (MT) codes and study some of their basic properties. Presenting several methods o...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2017
ISSN: 0024-3795
DOI: 10.1016/j.laa.2017.03.011