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Traceability codes
- Source :
-
Journal of Combinatorial Theory - Series A . Nov2010, Vol. 117 Issue 8, p1049-1057. 9p. - Publication Year :
- 2010
-
Abstract
- Abstract: Traceability codes are combinatorial objects introduced by Chor, Fiat and Naor in 1994 to be used in traitor tracing schemes to protect digital content. A k-traceability code is used in a scheme to trace the origin of digital content under the assumption that no more than k users collude. It is well known that an error correcting code of high minimum distance is a traceability code. When does this ‘error correcting construction’ produce good traceability codes? The paper explores this question. Let ℓ be a fixed positive integer. When q is a sufficiently large prime power, a suitable Reed–Solomon code may be used to construct a 2-traceability code containing codewords. The paper shows that this construction is close to best possible: there exists a constant c, depending only on ℓ, such that a q-ary 2-traceability code of length ℓ contains at most codewords. This answers a question of Kabatiansky from 2005. Barg and Kabatiansky (2004) asked whether there exist families of k-traceability codes of rate bounded away from zero when q and k are constants such that . These parameters are of interest since the error correcting construction cannot be used to construct k-traceability codes of constant rate for these parameters: suitable error correcting codes do not exist when because of the Plotkin bound. Kabatiansky (2004) answered Barg and Kabatiansky''s question (positively) in the case when . This result is generalised to the following: whenever k and q are fixed integers such that and , or such that and , there exist infinite families of q-ary k-traceability codes of constant rate. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 117
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 52935764
- Full Text :
- https://doi.org/10.1016/j.jcta.2010.02.009