Related papers: Lectures on DNA Codes
Binary similarity detection is a critical technique that has been applied in many real-world scenarios where source code is not available, e.g., bug search, malware analysis, and code plagiarism detection. Existing works are ineffective in…
DNA sequences encode critical genetic information, yet their variable length and discrete nature impede direct utilization in deep learning models. Existing DNA representation schemes convert sequences into numerical vectors but fail to…
Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the…
DNA-based storage is an emerging technology that enables digital information to be archived in DNA molecules. This method enjoys major advantages over magnetic and optical storage solutions such as exceptional information density, enhanced…
A code is called solid if, roughly speaking, any correctly-transmitted codeword in an arbitrarily corrupted string of codewords can still be decoded correctly and unambiguously. So-called variable-length solid codes, in which codewords may…
The problem of differentiating the informational content of coding (exons) and non-coding (introns) regions of a DNA sequence is one of the central problems of genomics. The introns are estimated to be nearly 95% of the DNA and since they…
Gene annotation has traditionally required direct comparison of DNA sequences between an unknown gene and a database of known ones using string comparison methods. However, these methods do not provide useful information when a gene does…
In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given…
In a distributed information application an encoder compresses an arbitrary vector while a similar reference vector is available to the decoder as side information. For the Hamming-distance similarity measure, and when guaranteed perfect…
The growing amount of data available in modern-day datasets makes the need to efficiently search and retrieve information. To make large-scale search feasible, Distance Estimation and Subset Indexing are the main approaches. Although binary…
In this paper, we describe a new type of DNA codes over two noncommutative rings $E$ and $F$ of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over $E$ and $F$. Using quasi self-duality, we can describe…
In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set of $M$ sequences, each of length $L$. Errors…
A basic problem for constant dimension codes is to determine the maximum possible size $A_q(n,d;k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$, called codewords, such that the subspace distance satisfies…
This paper considers cyclic DNA codes of arbitrary length over the ring $R=\F_2[u]/u^4-1$. A mapping is given between the elements of $R$ and the alphabet $\{A,C,G,T\}$ which allows the additive stem distance to be extended to this ring.…
A new numerical characterization of symbolic sequences is proposed. The partition of sequence based on Ke and Tong algorithm is a starting point. Algorithm decomposes original sequence into set of distinct subsequences - a patterns. The set…
A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes…
A decoding algorithm for $q$-ary low-density parity-check codes over the $q$-ary symmetric channel is introduced. The exchanged messages are lists of symbols from $\Fq$. A density evolution analysis for maximum list sizes $1$ and $2$ is…
Storing digital data in synthetic DNA faces challenges in ensuring data reliability in the presence of edit errors--deletions, insertions, and substitutions--that occur randomly during various stages of the storage process. Current…
DNA sequence alignment involves assigning short DNA reads to the most probable locations on an extensive reference genome. This process is crucial for various genomic analyses, including variant calling, transcriptomics, and epigenomics.…
Given $\mathbb{F}_q$ the finite field with $q$ elements and an integer $n\geq 2$, a flag is a sequence of nested subspaces of $\mathbb{F}_q^n$ and a flag code is a nonempty set of flags. In this context, the distance between flags is the…