A note on an upper bound of traceability codes. / Owen, Stephanie; Ng, Siaw-Lynn.

In: Australasian Journal of Combinatorics, Vol. 62, No. 1, 02.04.2015, p. 140-146.

Research output: Contribution to journalArticle

Published

Standard

A note on an upper bound of traceability codes. / Owen, Stephanie; Ng, Siaw-Lynn.

In: Australasian Journal of Combinatorics, Vol. 62, No. 1, 02.04.2015, p. 140-146.

Research output: Contribution to journalArticle

Harvard

Owen, S & Ng, S-L 2015, 'A note on an upper bound of traceability codes', Australasian Journal of Combinatorics, vol. 62, no. 1, pp. 140-146. <http://ajc.maths.uq.edu.au/pdf/62/ajc_v62_p140.pdf>

APA

Owen, S., & Ng, S-L. (2015). A note on an upper bound of traceability codes. Australasian Journal of Combinatorics, 62(1), 140-146. http://ajc.maths.uq.edu.au/pdf/62/ajc_v62_p140.pdf

Vancouver

Owen S, Ng S-L. A note on an upper bound of traceability codes. Australasian Journal of Combinatorics. 2015 Apr 2;62(1):140-146.

Author

Owen, Stephanie ; Ng, Siaw-Lynn. / A note on an upper bound of traceability codes. In: Australasian Journal of Combinatorics. 2015 ; Vol. 62, No. 1. pp. 140-146.

BibTeX

@article{bd2164d43a574d77800c690fa46d8545,
title = "A note on an upper bound of traceability codes",
abstract = "Blackburn, Etzion and Ng showed in a paper in 2010 that there exist 2-traceability codes of length l of size c ql/4 where the constant c dependsonly on l. The question remains as to what the best possible c may be. Awell-known construction using error-correcting codes with high minimumdistance gives 2-traceability codes of size c ql/4 with c ≥ 1. However, inthe same paper, an example of a 2-traceability code of length 3 withsize 3/2 (q − 1) was given, which shows that c > 1 in some situations, andthat there are traceability codes that are bigger than the constructionusing error-correcting codes. Here we give an upper bound 4q − 3 for 2-traceability codes of length 4 and give an example of (l − 1)-traceabilitycodes of length l with size (l/(l−1)) (q − 1). This example also gives a 2-traceability code of length 4 larger than any codes constructed using theerror-correcting code construction.",
keywords = "Traceability codes",
author = "Stephanie Owen and Siaw-Lynn Ng",
note = "This work was part of Stephanie Owen's MSc project at the School of Mathematics and Information Security, Royal Holloway, University of London.",
year = "2015",
month = apr,
day = "2",
language = "English",
volume = "62",
pages = "140--146",
journal = "Australasian Journal of Combinatorics",
issn = "1034-4942",
publisher = "University of Queensland Press",
number = "1",

}

RIS

TY - JOUR

T1 - A note on an upper bound of traceability codes

AU - Owen, Stephanie

AU - Ng, Siaw-Lynn

N1 - This work was part of Stephanie Owen's MSc project at the School of Mathematics and Information Security, Royal Holloway, University of London.

PY - 2015/4/2

Y1 - 2015/4/2

N2 - Blackburn, Etzion and Ng showed in a paper in 2010 that there exist 2-traceability codes of length l of size c ql/4 where the constant c dependsonly on l. The question remains as to what the best possible c may be. Awell-known construction using error-correcting codes with high minimumdistance gives 2-traceability codes of size c ql/4 with c ≥ 1. However, inthe same paper, an example of a 2-traceability code of length 3 withsize 3/2 (q − 1) was given, which shows that c > 1 in some situations, andthat there are traceability codes that are bigger than the constructionusing error-correcting codes. Here we give an upper bound 4q − 3 for 2-traceability codes of length 4 and give an example of (l − 1)-traceabilitycodes of length l with size (l/(l−1)) (q − 1). This example also gives a 2-traceability code of length 4 larger than any codes constructed using theerror-correcting code construction.

AB - Blackburn, Etzion and Ng showed in a paper in 2010 that there exist 2-traceability codes of length l of size c ql/4 where the constant c dependsonly on l. The question remains as to what the best possible c may be. Awell-known construction using error-correcting codes with high minimumdistance gives 2-traceability codes of size c ql/4 with c ≥ 1. However, inthe same paper, an example of a 2-traceability code of length 3 withsize 3/2 (q − 1) was given, which shows that c > 1 in some situations, andthat there are traceability codes that are bigger than the constructionusing error-correcting codes. Here we give an upper bound 4q − 3 for 2-traceability codes of length 4 and give an example of (l − 1)-traceabilitycodes of length l with size (l/(l−1)) (q − 1). This example also gives a 2-traceability code of length 4 larger than any codes constructed using theerror-correcting code construction.

KW - Traceability codes

M3 - Article

VL - 62

SP - 140

EP - 146

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

IS - 1

ER -