New results on DNA codes

D’yachkov, Arkadii G.; Macula, Anthony J.; Renz, Thomas E.; Vilenkin, Pavel A.; Ismagilov, I. K.

doi:10.1109/isit.2005.1523339

Cited by 12 publications

(5 citation statements)

References 9 publications

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“…Next, we give the definitions of two different maps. Let C be a code over R of length n, ξ is a Gray map from R to R 3 1 such that a…”

Section: Dna Codes Over the Ring Rmentioning

confidence: 99%

“…In [1,9,11], cyclic DNA codes over finite fields with four and sixteen elements were considered, respectively. Further, in [12], Siap I et al considered cyclic DNA codes over the ring F 2 [u]/ u 2 − 1 based on the deletion distance and there were also a lot of progress about cyclic DNA codes over the ring, the more information can be seen in [3,4,6,7,13]. Motivated by the work listed above, we are interested in cyclic DNA codes over the ring R. In this work, we construct the cyclic DNA codes over the ring…”

Section: Introductionmentioning

confidence: 99%

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Cyclic DNA codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_2[u,v]/\langle u^3, v^2-v, vu-uv\rangle$\end{document}</tex-math></inline-formula>

Shi¹,

Lu²

2019

Advances in Mathematics of Communications

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“…Next, we give the definitions of two different maps. Let C be a code over R of length n, ξ is a Gray map from R to R 3 1 such that a…”

Section: Dna Codes Over the Ring Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cyclic DNA codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_2[u,v]/\langle u^3, v^2-v, vu-uv\rangle$\end{document}</tex-math></inline-formula>

Shi¹,

Lu²

2019

Advances in Mathematics of Communications

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“…Slightly stronger bounds are given in [33]. A simple construction of cover-free families is based on concatenated codes [7,8,9,10].…”

Section: Cover-free Familiesmentioning

confidence: 99%

An Efficient Single-Key Pirates Tracing Scheme Using Cover-Free Families

Tonien

2006

Lecture Notes in Computer Science

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A cover-free family is a well-studied combinatorial structure that has many applications in computer science and cryptography. In this paper, we propose a new public key traitor tracing scheme based on cover-free families. The new traitor tracing scheme is similar to the Boneh-Franklin scheme except that in the BonehFranklin scheme, decryption keys are derived from Reed-Solomon codes while in our case they are derived from a cover-free family. This results in much simpler and faster tracing algorithms for single-key pirate decoders, compared to the tracing algorithms of Boneh-Franklin scheme that use Berlekamp-Welch algorithm. Our tracing algorithms never accuse innocent users and identify all traitors with overwhelming probability. Abstract A cover-free family is a well-studied combinatorial structure that has many applications in computer science and cryptography. In this paper, we propose a new public key traitor tracing scheme based on cover-free families. The new traitor tracing scheme is similar to the BonehFranklin scheme except that in the Boneh-Franklin scheme, decryption keys are derived from Reed-Solomon codes while in our case they are derived from a cover-free family. This results in much simpler and faster tracing algorithms for single-key pirate decoders, compared to the tracing algorithms of Boneh-Franklin scheme that use Berlekamp-Welch algorithm. Our tracing algorithms never accuse innocent users and identify all traitors with overwhelming probability.

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“…Later attempts included deletion similarity [8], which was earlier introduced by Levenshtein [17] and block similarity [12]- [13]. Both functions are non-additive which allowed for consideration of such cases as shifts of DNA sequences along each other.…”

Section: Introductionmentioning

confidence: 99%

On critical relative distance of DNA codes for additive stem similarity

D’yachkov

Voronina

Macula

et al. 2010

2010 IEEE International Symposium on Information Theory

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Abstract-We consider DNA codes based on the nearestneighbor (stem) similarity model which adequately reflects the "hybridization potential" of two DNA sequences. Our aim is to present a survey of bounds on the rate of DNA codes with respect to a thermodynamically motivated similarity measure called an additive stem similarity. These results yield a method to analyze and compare known samples of the nearest neighbor "thermodynamic weights" associated to stacked pairs that occurred in DNA secondary structures.

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New results on DNA codes

Cited by 12 publications

References 9 publications

Cyclic DNA codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_2[u,v]/\langle u^3, v^2-v, vu-uv\rangle$\end{document}</tex-math></inline-formula>

Cyclic DNA codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_2[u,v]/\langle u^3, v^2-v, vu-uv\rangle$\end{document}</tex-math></inline-formula>

An Efficient Single-Key Pirates Tracing Scheme Using Cover-Free Families

On critical relative distance of DNA codes for additive stem similarity

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