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Separating Codes: Constructions and Bounds
[chapter]
2004
Lecture Notes in Computer Science
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Separating codes play their role in making the fingerprinting scheme secure agains coalitions of pirates. We provide here better bounds, constructions and generalizations for these codes. ...
Separating codes, initially introduced to test automaton, have revived lately in the study of fingerprinting codes, which are used for copyright protection. ...
There is a constructive asymptotic family of binary (2, 1)-separating codes with rate R = 0.1845. ...
doi:10.1007/978-3-540-24698-5_36
fatcat:rwjnd2mqejeqvcinhynmzvyehu
Bounds and Constructions for 3-Strongly Separable Codes with Length 3
[article]
2017
arXiv
pre-print
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Codes and Cryptogr.79:303-318, 2016) can be also used to construct anti-collusion codes. ...
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. ...
FA380009 and CA380021) and 2014GXNSFDA(No. 118001). ...
arXiv:1611.04349v2
fatcat:o72rnae56jdwnc7klah4kjifta
Bounds and Constructions for 3-Separable Codes with Length 3
[article]
2015
arXiv
pre-print
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In this paper, an upper bound on M(3,3,q) is derived by considering an optimization problem related to a partial Latin square, and then two constructions for 3-SC(3,M,q)s are provided by means of perfect ...
C is a t-separable code if for any two distinct C_1, C_2 ⊆C with |C_1| < t, |C_2| < t, we always have desc(C_1) ≠ desc(C_2). Let M(t,n,q) denote the maximal possible size of such a separable code. ...
Cheng and Miao [8] showed that long-length separable codes can be constructed by concatenating short-length separable codes. ...
arXiv:1507.00954v1
fatcat:yoexz3slgze3ramzl3exrwzuxa
Separating hash families: A Johnson-type bound and new constructions
[article]
2016
arXiv
pre-print
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In this paper, using tools from graph theory and additive number theory, we solve several open problems and conjectures concerning bounds and constructions for separating hash families. ...
Secondly, we present a construction for an infinite class of perfect hash families. It is based on the Hamming graphs in coding theory and generalizes many constructions that appeared before. ...
We call this recursive bound a "Johnson-type bound" due to its similarity with the traditional recursive Johnson bound in coding theory. ...
arXiv:1601.04807v2
fatcat:5gew5eemzrdhhmo4rcc26f73kq
Constructions and Bounds for Mixed-Dimension Subspace Codes
[article]
2018
arXiv
pre-print
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For d=v-2 we present some improved bounds and determine A_q(5,3)=2q^3+2 (all q), A_2(7,5)=34. ...
We also provide an exposition of the known determination of A_q(v,2), and a table with exact results and bounds for the numbers A_2(v,d), v≤ 7. ...
Acknowledgments The authors are grateful to Tuvi Etzion for comments regarding the upper bound in Theorem 4.1 and to two anonymous reviewers for valuable comments and corrections. ...
arXiv:1512.06660v3
fatcat:4z2j5tcrnnf6rkueixorzdkkxi
Construction and bounds for subspace codes
[article]
2021
arXiv
pre-print
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They have e.g. applications in random linear network coding, distributed storage, and cryptography. In this chapter we survey known constructions and upper bounds for subspace codes. ...
Subspace codes are the q-analog of binary block codes in the Hamming metric. Here the codewords are vector spaces over a finite field. ...
57
5 Constructions for constant dimension codes
5.4 Constructions for 𝑑 -packings of CDCs and RMCs
As already mentioned, we can separate the problem of the choice of the ...
arXiv:2112.11766v1
fatcat:u4l2josijvg2nk5sttu5zgnbh4
Matroid Theory and Storage Codes: Bounds and Constructions
[article]
2017
arXiv
pre-print
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Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs). ...
The chapter embeds all the essential features of LRCs, namely locality, availability, and hierarchy alongside with related generalised Singleton bounds. ...
The first example of a storage code, and the motivating example behind the notion of locality, is the notion of a maximum distance separable (MDS) code. ...
arXiv:1704.04007v2
fatcat:vzvtotomevgxhhbxo5otfaosbq
Bounds and Constructions for Multi-Symbol Duplication Error Correcting Codes
[article]
2018
arXiv
pre-print
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Finally, we discuss the asymptotic behavior of the derived codes and bounds, which yields insights about the tandem duplication channel. ...
Based on the fact that a code correcting insertions of t zero-blocks can be used to correct t tandem duplications, we construct codes for tandem duplication errors. ...
We have further found two constructions can correct Fig. 1 .Fig. 2 . 12 Redundancy of constructions and bounds (p = 2, t = 1, ℓ = 3) Redundancy of constructions and bounds (p = 2, t = 3, ℓ = 3)
This ...
arXiv:1807.02874v3
fatcat:pdnxgforozfjvfpzkdneelxukq
Bounds and Constructions for Multireceiver Authentication Codes
[chapter]
1998
Lecture Notes in Computer Science
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In this paper, we give a formal definition of multireceiver authentication codes, derive information theoretic and combinatorial lower bounds on their performance and give new efficient constructions for ...
such codes, our constructions are based on the linear error-correcting codes. ...
Using maximum distance separable codes in the first construction, and special values for parameters in the second, results in new optimal MRA-codes that satisfy lower bounds on the size of keys and the ...
doi:10.1007/3-540-49649-1_20
fatcat:gm2vzx34zndetekdnw5tvrobnq
Refined Coding Bounds and Code Constructions for Coherent Network Error Correction
2011
IEEE Transactions on Information Theory
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The tightness of this refined bound is shown by two construction algorithms of linear network codes achieving this bound. ...
With respect to a given set of local encoding kernels defining a linear network code, we obtain refined versions of the Hamming bound, the Singleton bound and the Gilbert-Varshamov bound for coherent network ...
The relation between network coding and maximum distance separation (MDS) codes in classical algebraic coding [14] was clarified in [15] . ...
doi:10.1109/tit.2011.2106930
fatcat:sxlq6ls5szgy5f2hkaupt445ge
Bounds and Constructions of Codes with Multiple Localities
[article]
2016
arXiv
pre-print
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This paper studies bounds and constructions of locally repairable codes (LRCs) with multiple localities so-called multiple-locality LRCs (ML-LRCs). ...
Furthermore, we construct Singleton-optimal ML-LRCs as well as codes that achieve the extended alphabet-dependent bound. ...
For r ≥ k Thm. 2 coincides with the classical (locality-unaware) Singleton bound and then a Singleton-optimal code is called maximum distance separable (MDS). ...
arXiv:1601.02763v1
fatcat:d4zrypona5dx7mipq6w6v2g3ly
New LMRD bounds for constant dimension codes and improved constructions
[article]
2018
arXiv
pre-print
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We generalize upper bounds for constant dimension codes containing a lifted maximum rank distance code first studied by Etzion and Silberstein. The proof allows to construct several improved codes. ...
A prominent code construction uses maximum rank distance (MRD) codes. ...
[2, 23] often surpasses the LMRD bound and is therefore stronger than all constructions that include an LMRD as subset. ...
arXiv:1801.04803v1
fatcat:5ndpcusfcnclffpfy2pby7woqa
Bounds and constructions of codes with multiple localities
2016
2016 IEEE International Symposium on Information Theory (ISIT)
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This paper studies bounds and constructions of locally repairable codes (LRCs) with multiple localities so-called multiplelocality LRCs (ML-LRCs). ...
Furthermore, we construct Singleton-optimal ML-LRCs as well as codes that achieve the extended alphabet-dependent bound. ...
For r ≥ k Thm. 2 coincides with the classical (locality-unaware) Singleton bound and then a Singleton-optimal code is called maximum distance separable (MDS). ...
doi:10.1109/isit.2016.7541377
dblp:conf/isit/ZehY16
fatcat:shljnhm4fvcdnlmn42mzfonpga
Constacyclic symbol-pair codes: lower bounds and optimal constructions
[article]
2016
arXiv
pre-print
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First we present three lower bounds for the minimum pair distance of constacyclic codes, the first two of which generalize the previously known results due to Cassuto and Blaum (2011) and Kai et al. (2015 ...
The third one exhibits a lower bound for the minimum pair distance of repeated-root cyclic codes. ...
The aforementioned works lead us to the study of lower bounds for the minimum pair distance of constacyclic codes and constructions of MDS symbol-pair codes. ...
arXiv:1605.03460v1
fatcat:xxdxny6thvdn3ox7wcu7so3ykq
Improved Singleton bound on insertion-deletion codes and optimal constructions
[article]
2021
arXiv
pre-print
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bound were also constructed explicitly. ...
Haeupler and Shahrasbi established the Singleton bound for insdel codes: the minimum insdel distance of any [n,k] linear code over 𝔽_q satisfies d≤2n-2k+2. ...
The aforementioned works lead us to the study of Singleton-type bounds for the minimum insdel distance of general linear codes and optimal constructions of such codes. ...
arXiv:2105.02004v1
fatcat:vsywd2lewjfyjevbso6awnqgfm
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