Codes from hall planes of odd order

J. D. Key; T. P. McDonough; V. C. Mavron

doi:10.3934/amc.2017011

Codes from hall planes of odd order

J. D. Key, T. P. McDonough, V. C. Mavron

Adran Mathemateg

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

Crynodeb

We show explicitly that the dimension of the ternary code of the Hall plane of order 9 is greater than the dimension of the ternary code of the desarguesian plane of order 9. The proof requires finding a word with some defined properties in the dual ternary code of the desarguesian plane of order 9. The idea can be generalised for other orders, provided that words in the dual code of the desarguesian projective plane that have the specified properties can be found.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	179-185
Nifer y tudalennau	7
Cyfnodolyn	Advances in Mathematics of Communications
Cyfrol	11
Rhif cyhoeddi	1
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.3934/amc.2017011
Statws	Cyhoeddwyd - 01 Chwef 2017

Mynediad at Ddogfen

10.3934/amc.2017011

Cysylltiad parhaol

Dolen barhaus

Ffeiliau eraill a chysylltiadau

Link to publication in Scopus

Dyfynnu hyn

@article{148404cb3ff74a73ab6d30b540a81392,

title = "Codes from hall planes of odd order",

abstract = "We show explicitly that the dimension of the ternary code of the Hall plane of order 9 is greater than the dimension of the ternary code of the desarguesian plane of order 9. The proof requires finding a word with some defined properties in the dual ternary code of the desarguesian plane of order 9. The idea can be generalised for other orders, provided that words in the dual code of the desarguesian projective plane that have the specified properties can be found.",

keywords = "Codes, Hamada-Sachar conjecture, Non-desarguesian planes",

author = "Key, {J. D.} and McDonough, {T. P.} and Mavron, {V. C.}",

year = "2017",

month = feb,

day = "1",

doi = "10.3934/amc.2017011",

language = "English",

volume = "11",

pages = "179--185",

journal = "Advances in Mathematics of Communications",

issn = "1930-5346",

publisher = "American Institute of Mathematical Sciences",

number = "1",

}

TY - JOUR

T1 - Codes from hall planes of odd order

AU - Key, J. D.

AU - McDonough, T. P.

AU - Mavron, V. C.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We show explicitly that the dimension of the ternary code of the Hall plane of order 9 is greater than the dimension of the ternary code of the desarguesian plane of order 9. The proof requires finding a word with some defined properties in the dual ternary code of the desarguesian plane of order 9. The idea can be generalised for other orders, provided that words in the dual code of the desarguesian projective plane that have the specified properties can be found.

AB - We show explicitly that the dimension of the ternary code of the Hall plane of order 9 is greater than the dimension of the ternary code of the desarguesian plane of order 9. The proof requires finding a word with some defined properties in the dual ternary code of the desarguesian plane of order 9. The idea can be generalised for other orders, provided that words in the dual code of the desarguesian projective plane that have the specified properties can be found.

KW - Codes

KW - Hamada-Sachar conjecture

KW - Non-desarguesian planes

UR - http://www.scopus.com/inward/record.url?scp=85013018451&partnerID=8YFLogxK

U2 - 10.3934/amc.2017011

DO - 10.3934/amc.2017011

M3 - Article

AN - SCOPUS:85013018451

SN - 1930-5346

VL - 11

SP - 179

EP - 185

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

IS - 1

ER -

Codes from hall planes of odd order

Crynodeb

Mynediad at Ddogfen

Cysylltiad parhaol

Ffeiliau eraill a chysylltiadau

Ôl bys

Dyfynnu hyn