Flag codes of maximum distance and constructions using Singer groups
نویسندگان
چکیده
In this paper we study flag codes of maximum distance. We characterize these in terms of, at most, two relevant constant dimension naturally associated to them. do first for general and then particularize those arising as orbits under the action arbitrary subgroups linear group. provide different systematic orbital constructions attaining both distance size. To end, use Singer groups take advantage good relation between Desarguesian spreads, well fact that they act transitively on lines hyperplanes.
منابع مشابه
Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes
Symbol-pair code is a new coding framework which is proposed to correct errors in the symbolpair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pairdistance five or six. ...
متن کاملOptical Orthogonal Codes from Singer Groups
We construct some new families of optical orthogonal codes that are asymptotically optimal. In particular, for any prescribed value of λ, we construct infinite families of (n, w, λ)-OOCs that in each case are asymptotically optimal. Our constructions rely on various techniques in finite projective spaces involving normal rational curves and Singer groups. These constructions generalize and impr...
متن کاملMaximum distance q -nary codes
t immaru-A q-nary error-correcting code with N = qk code words of length n = k + r can have no greater miniium distance d than r + 1. The class of codes for which d = r + 1 is studied first in general, then with the restriction that the codes be linear. Examples and construction methods are given to show that these codes exist for a number of values of q, k, and r. Proof: Pick any k position. T...
متن کامل2-dimensional Optical Orthogonal Codes from Singer Groups
We present several new families of (Λ × T,w, λ) (2-D) wavelength/time optical orthogonal codes (2D-OOCs) with λ = 1, 2. All families presented are either optimal with respect to the Johnson bound (J-optimal) or are asymptotically optimal. The codes presented have more flexible dimensions and weight than the J-optimal families appearing in the literature. The constructions are based on certain p...
متن کاملCyclic Orbit Codes with the Normalizer of a Singer Subgroup
An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2022
ISSN: ['1090-2465', '1071-5797']
DOI: https://doi.org/10.1016/j.ffa.2022.102011