A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Small weight codewords in the codes arising from Desarguesian projective planes

2007
*
Designs, Codes and Cryptography
*

We study

doi:10.1007/s10623-007-9126-x
fatcat:4p5jprjpp5hffg475wqpquo5im
*codewords*of*small**weight**in**the**codes**arising**from**Desarguesian**projective**planes*. We first of all improve*the*results of K. ... Chouinard on*codewords*of*small**weight**in**the**codes**arising**from*P G(2, p), p prime. Chouinard characterized all*the**codewords*up to*weight*2p*in*these*codes*. ... For arbitrary*Desarguesian**projective**planes*, we give a discrete spectrum for*the*possible*weights*of*the**codewords**in**the*interval [q + 2, 3q/2] and exclude all*codewords*with*weight**in**the*interval [ ...##
###
On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual

2008
*
Designs, Codes and Cryptography
*

We link

doi:10.1007/s10623-008-9203-9
fatcat:qkjipzxtrrc5hhpa5zddv5oyv4
*the**codewords*of*small**weight*of this*code*to blocking sets with respect to lines*in*P G(n, q) and we exclude all possible*codewords**arising**from**small*linear blocking sets. ...*In*this paper, we study*the*p-ary linear*code*C(P G(n, q)), q = p h , p prime, h ≥ 1, generated by*the*incidence matrix of points and hyperplanes of a*Desarguesian**projective*space P G(n, q), and its dual ... Acknowledgement:*The*authors wish to thank*the*referees for their detailed reading of this article and for their valuable suggestions for improvement. ...##
###
On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual
[article]

2012
*
arXiv
*
pre-print

We link

arXiv:1201.3290v1
fatcat:nhd2z3biwzawdasnzz4st3d6qe
*the**codewords*of*small**weight*of this*code*to blocking sets with respect to lines*in*PG(n, q) and we exclude all possible*codewords**arising**from**small*linear blocking sets. ...*In*this paper, we study*the*p-ary linear*code*C(PG(n, q)), q = p^h, p prime, h >= 1, generated by*the*incidence matrix of points and hyperplanes of a*Desarguesian**projective*space PG(n, q), and its dual ... Acknowledgement:*The*authors wish to thank*the*referees for their detailed reading of this article and for their valuable suggestions for improvement. ...##
###
An upper bound for the minimum weight of the dual codes of desarguesian planes

2009
*
European journal of combinatorics (Print)
*

We show that a construction described

doi:10.1016/j.ejc.2008.01.003
fatcat:mflozklhfzbdnjtxodp5iutet4
*in*Clark, Key and de Resmini [9] of*small*-*weight*words*in**the*dual*codes*of finite translation*planes*can be extended so that it applies to*projective*and affine*desarguesian*... This gives words of*weight*2p m + 1 − p m −1 p−1*in**the*dual of*the*p-ary*code*of*the**desarguesian**plane*of order p m , and provides an improved upper bound for*the*minimum*weight*of*the*dual*code*. ... For*planes*of*small*non-prime odd order,*the*dual ternary*codes*of*the*four*projective**planes*of order 9 were shown*in*[16] to all have d ⊥ = 15 apart*from**the*Hughes*plane*, for which d ⊥ = 14. ...##
###
Moderate Density Parity-Check Codes from Projective Bundles
[article]

2021
*
arXiv
*
pre-print

We design a parity-check matrix for this family of binary

arXiv:2103.09722v1
fatcat:tsvuul4l3zedfggz5klvs6pj2m
*codes*as*the*concatenation of two matrices:*the*incidence matrix between points and lines of*the**Desarguesian**projective**plane*and*the*incidence ...*In*this setting, our*codes*have*the*best possible error-correction performance for this range of parameters. ... Acknowledgment*The*work of A. Neri was supported by*the*Swiss National Science Foundation through grant no. 187711.*The*work of J. ...##
###
Small weight codewords in the LDPC codes arising from linear representations of geometries

2009
*
Journal of combinatorial designs (Print)
*

*In*this paper, we investigate

*the*minimum distance and

*small*

*weight*

*codewords*of

*the*LDPC

*codes*of linear representations, using only geometrical methods. ... When investigating

*the*

*small*

*weight*

*codewords*of T * 2 (Θ) D , we deal with

*the*case of Θ a regular hyperoval, i.e. a conic and its nucleus, separately, since

*in*this case, we have a larger upper bound ...

*The*goal of this section is to characterize

*small*

*weight*

*codewords*of

*the*q-ary LDPC

*code*C

*arising*

*from*T * 2 (Θ), with q = 2 h , by using geometrical arguments. ...

##
###
Scattered Spaces in Galois Geometry
[article]

2016
*
arXiv
*
pre-print

This is a survey paper on

arXiv:1512.05251v2
fatcat:xhhabrelpzazvi45fjgvprcbt4
*the*theory of scattered spaces*in*Galois geometry and its applications. ...*The*author thanks*the*members of*the*Algebra group of Sabancı University for their hospitality and*the*anonymous referees for their comments and suggestions. ... For non-*Desarguesian**projective**planes*, and*in*particular for translation*planes*,*the*classification remains open. ...##
###
Partitions in finite geometry and related constant composition codes

2008
*
Innovations in Incidence Geometry Algebraic Topological and Combinatorial
*

We look at

doi:10.2140/iig.2008.8.49
fatcat:q7emi2h775fj7b3zv5n2qg373q
*the*construction of constant composition*codes*(CCCs)*from*various types of partitions*in*finite*projective*spaces. ...*In*addition, we examine other partitions of objects embedded*in*finite*projective*spaces and their associated*codes*. ...*The*authors would like to thank Norm Johnson for his guidance regarding*the*proof of Theorem 2.6. ...##
###
On the code generated by the incidence matrix of points and k-spaces in PG(n, q) and its dual
[article]

2012
*
arXiv
*
pre-print

We first prove that such a k-blocking set is uniquely reducible to a minimal k-blocking set, and exclude all

arXiv:1201.3291v1
fatcat:6lo5viimajboxidjrbzkawqyp4
*codewords**arising**from**small*linear k-blocking sets. ... Next, we study*the*dual*code*of Ck(n, q) and present a lower bound on*the**weight*of*the**codewords*, hence extending*the*results of Sachar [12] to general dimension. ...*the**codewords*of*small**weight**in**the*p-ary linear*code*generated by*the*incidence matrix of points and k-dimensional spaces, or for short k-spaces,*in*P G(n, q), q = p h , p prime, h ≥ 1. ...##
###
On the code generated by the incidence matrix of points and k-spaces in PG(n,q) and its dual

2008
*
Finite Fields and Their Applications
*

We first prove that such a k-blocking set is uniquely reducible to a minimal k-blocking set, and exclude all

doi:10.1016/j.ffa.2008.06.002
fatcat:hpifrjnznna5nmdvv5fyle3wcq
*codewords**arising**from**small*linear k-blocking sets. ... Next, we study*the*dual*code*of C k (n, q) and present a lower bound on*the**weight*of*the**codewords*, hence extending*the*results of Sachar [H. ...*the**codewords*of*small**weight**in**the*p-ary linear*code*generated by*the*incidence matrix of points and k-dimensional spaces, or for short k-spaces,*in*PG(n, q), q = p h , p prime, h 1. ...##
###
Small sets of even type and codewords

1998
*
Journal of Geometry
*

*In*particular we look at

*small*sets of points

*in*

*projective*

*planes*of even order that are met evenly by all

*the*lines of

*the*

*plane*, and find vectors of

*small*

*weight*

*in*

*the*binary hull and

*in*

*the*code's ... We examine some geometric configurations of points

*in*designs that give rise to vectors

*in*

*the*

*codes*associated with

*the*designs. ... and

*the*first author would like to thank

*the*Dipartimento di Matematica at

*the*Universitá di Roma 'La Sapienza' for their hospitality, and

*the*C.N.R. ...

##
###
Some Applications of Magma in Designs and Codes: Oval Designs, Hermitian Unitals and Generalized Reed–Muller Codes

2001
*
Journal of symbolic computation
*

We describe three applications of Magma to problems

doi:10.1006/jsco.1999.1007
fatcat:4x6vyvqhq5dk3jpxi2mfzkf3qy
*in**the*area of designs and*the*associated*codes*: • Steiner systems, Hadamard designs and symmetric designs*arising**from*a oval*in*an even order*plane*... , leading*in**the*classical case to bent functions and difference-set designs; •*the*hermitian unital as a 2-(q 3 + 1, q + 1, 1) design, and*the**code*over F p where p divides q + 1; • a basis of minimum-*weight*... Acknowledgement:*The*author would like to thank*the*Department of Computer Science and Engineering and*the*Center for Communication and Information Science (CCIS) at*the*University of Nebraska for their ...##
###
\begin{document}$ s $\end{document}-PD-sets for codes from projective planes \begin{document}$ \mathrm{PG}(2,2^h) $\end{document}, \begin{document}$ 5 \leq h\leq 9 $\end{document}

2019
*
Advances in Mathematics of Communications
*

*In*this paper we construct 2-PD-sets of 16 elements for

*codes*

*from*

*the*

*Desarguesian*

*projective*

*planes*PG(2, q), where q = 2 h and 5 ≤ h ≤ 9. ... We also construct 3-PD-sets of 75 elements for

*the*

*code*

*from*

*the*

*Desarguesian*

*projective*

*plane*PG(2, q), where q = 2 9 . ...

*The*research of D. Crnković and N. Mostarac has been supported by

*the*Croatian Science Foundation under

*the*

*project*6732. ...

##
###
On the history of ring geometry (with a thematical overview of literature)
[article]

2020
*
arXiv
*
pre-print

*In*this survey paper we give an historical and at

*the*same time thematical overview of

*the*development of ring geometry

*from*its origin to

*the*current state of

*the*art. ... A comprehensive up-to-date list of literature is added with articles that treat ring geometry within

*the*scope of incidence geometry. ... Another aspect that appears

*in*

*the*literature is

*the*correspondence between two-

*weight*

*codes*and strongly regular graphs. ...

##
###
The Use of Blocking Sets in Galois Geometries and in Related Research Areas
[chapter]

2011
*
Springer Proceedings in Mathematics
*

Besides their intrinsic geometrical importance,

doi:10.1007/978-1-4614-0709-6_15
fatcat:ngfvmymvprbqfooj4do3jadnb4
*the*importance of blocking sets also*arises**from**the*use of blocking sets for*the*solution of many other geometrical problems, and problems*in*related research ... By showing*the*many applications on blocking sets, we also wish to prove that researchers who improve results on blocking sets*in*fact open*the*door to improvements on*the*solution of many other problems ... One might wonder where all these Baer subplanes of holes*in*these poor*planes**arise**from*. ...
« Previous

*Showing results 1 — 15 out of 43 results*