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

Research output: Contribution to journal › Article

Published

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

Research output: Contribution to journal › Article

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.

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

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.

@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 = "4",

day = "2",

language = "English",

volume = "62",

pages = "140--146",

journal = "Australasian Journal of Combinatorics",

issn = "1034-4942",

publisher = "University of Queensland Press",

number = "1",

}

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 -