Asymptotically optimal 2 ¯ $\overline {2}$ -separable codes with length 4

Cheng, Minquan; Jiang, Jing; Tang, Xiaohu

doi:10.1007/s12095-016-0182-9

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Suppose that S is a subset of F n q 1 , of which no three distinct elements are collinear. Then equations (6), (7) and (8) have no solution in S. This implies that C does not contain △ 1 , △ 2 and △ 3 . Together with (10), we have the following result.…”

Section: Constructionmentioning

confidence: 99%

Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable codes with length 3

2017

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As separable code (SC, IEEE Trans Inf Theory 57:4843-4851, 2011) and frameproof code (FPC, IEEE Trans Inf Theory 44:1897-1905, 1998) do in multimedia fingerprinting, strongly separable code (SSC, Des. Codes and Cryptogr.79:303-318, 2016) can be also used to construct anti-collusion codes. Furthermore, SSC is better than FPC and SC in the applications for multimedia fingerprinting since SSC has lower tracing complexity than that of SC (the same complexity as FPC) and weaker structure than that of FPC. In this paper, we first derive several upper bounds on the number of codewords of t-SSC. Then we focus on 3-SSC with codeword length 3, and obtain the following two main results: (1) An equivalence between an SSC and an SC. (2) An improved lower bound Ω(q 5/3 + q 4/3 − q) on the size of a q-ary SSC when q = q 6 1 for any prime power q 1 ≡ 1 (mod 6), better than the before known bound ⌊ √ q⌋ 3 , which is obtained by means of difference matrix and the known result on the subset of F n q containing no three points on a line.

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Section: Constructionmentioning

confidence: 99%

Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable codes with length 3

2017

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“…As an important class of anti-collusion codes in multimedia copyright protection, separable codes and frameproof codes were widely studied, e.g., [3,5,6,7,8,9,11].…”

Section: Upper Bounds On M(t N Q)mentioning

confidence: 99%

Bounds and Constructions for $\overline{3}$-Strongly Separable Codes with Length $3$

Zhang¹,

Jiang²,

Cheng³

2016

Preprint

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can be also used to construct anti-collusion codes. Furthermore, SSC is better than FPC and SC in the applications for multimedia fingerprinting since SSC has lower tracing complexity than that of SC (the same complexity as FPC) and weaker structure than that of FPC. In this paper, we first derive several upper bounds on the number of codewords of t-SSC. Then we focus on 3-SSC with codeword length 3, and obtain the following two main results: (1) An equivalence between an SSC and an SC. (2) An improved lower bound Ω(q 5/3 + q 4/3 − q) on the size of a q-ary SSC when q = q 6 1 for any prime power q 1 ≡ 1 (mod 6), better than the before known bound ⌊ √ q⌋ 3 , which is obtained by means of difference matrix and the known result on the subset of F n q containing no three points on a line.

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2¯-separable codes with length 5

Wen

Jiang

2023

Discrete Mathematics

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Asymptotically optimal 2 ¯ $\overline {2}$ -separable codes with length 4

Cited by 3 publications

References 12 publications

Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable codes with length 3

Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable codes with length 3

Bounds and Constructions for $\overline{3}$-Strongly Separable Codes with Length $3$

2¯-separable codes with length 5

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