Finite projective geometries and linear codes
WebAn Enumeration of Certain Projective Ternary Two‐Weight Codes. Michael Martis, J. Bamberg, Sylvia Morris. Mathematics. 2014. We detail the enumeration of all two‐intersection sets of the five‐dimensional projective space over the field of order 3 that are invariant under an element of order 7, which include the examples of…. 8. WebMay 27, 2015 · Check Pages 1-48 of Finite Projective Geometries and Linear Codes in the flip PDF version. Finite Projective Geometries and Linear Codes was published by on 2015-05-27. Find more similar flip PDFs like Finite Projective Geometries and Linear Codes. Download Finite Projective Geometries and Linear Codes PDF for free.
Finite projective geometries and linear codes
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WebMar 1, 2010 · The shortest possible length of a q -ary linear code of covering radius R and codimension r is called the length function and is denoted by q ( r , R ). Constructions of codes with covering radius 3 are here developed, which improve best ... Web1.7. Finite Geometries 6 Note. Notice that Theorems 1.7.7 to 1.7.10 do not insure the existence of any particular structures, but instead are a conditional result. From these results, we see that the number n of points on a line determines several properties of a finite projective geometry. O. Veblen and W. H. Bussey published “Finite ...
WebMar 7, 2024 · Axiom: Projective Geometry. A line lies on at least two points. Any two distinct points have exactly one line in common. Any two distinct lines have at least one point in common. There is a set of four distinct points no three of which are colinear. All but one point of every line can be put in one-to-one correspondence with the real numbers. WebApr 7, 2009 · The first half of the book contains background material in design theory, including symmetric designs and designs from affine and projective geometry, and in coding theory, coverage of most of the important classes of linear codes. In particular, the authors provide a new treatment of the Reed-Muller and generalized Reed-Muller codes.
WebThese results have been found using a computer-based exhaustive search that exploits projective equivalence properties. Minimal 1-saturating sets in the projective plane PG(2, q) are considered. The classification of all the minimal 1-saturating sets in PG(2, q) for q ≤ 8, the classification of the smallest minimal 1-saturating sets in PG(2, q), 9 ≤ q ≤ 13 and the … WebIn this paper, let $ q $ be a power of a prime, we construct several classes of new projective three-weight or four-weight linear codes over $ \mathbb{F}_q $ from the defining sets construction, and determine their weight distributions by using additive character sums. Especially, these codes are suitable for applications in secret sharing schemes.
WebLINEAR REPRESENTATIONS OF FINITE GEOMETRIES AND ASSOCIATED LDPC CODES. PETER SIN, JULIEN SORCI AND QING XIANG Abstract. The linear representation of a subset of a nite projective space is an incidence system of a ne points and lines determined by the subset. In this paper we use character theory to show that …
WebFor a basic introduction to projective geometry see [2]. 2 Basic Defintions and results Let’s start with the definition of a projective plane. Definition 2.1. A Projective plane Pis an ordered pair of sets (p(P);l(P)), whose elements are called points and lines, respectively, and a relation between these sets, called incidence, personal finance option put definitionWebAug 19, 2024 · Title:Linear representations of finite geometries and associated LDPC codes Authors:Peter Sin, Julien Sorci, Qing Xiang Download PDF Abstract:The {\it … standard chartered bank sanctions fineWebNov 20, 2024 · An explicit construction will be given for such a set of collineations with the aid of primitive elements of Galois fields. This leads to a calculus for the linear … standard chartered bank scblinbbxxx