相关论文: On DNA Codes Over the Non-Chain Ring $\mathbb{Z}_4…

We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on…

For $q$-ary $n$-sequences, we develop the concept of similarity functions that can be used (for $q=4$) to model a thermodynamic similarity on DNA sequences. A similarity function is identified by the length of a longest common subsequence…

The sequence-dependent elasticity of double-helical DNA on a nm length scale can be captured by the rigid base-pair model, whose strains are the relative position and orientation of adjacent base-pairs. Corresponding elastic potentials have…

In the recent years, DNA has emerged as a potentially viable storage technology. DNA synthesis, which refers to the task of writing the data into DNA, is perhaps the most costly part of existing storage systems. Accordingly, this high cost…

Data storage in DNA is developing as a possible solution for archival digital data. Recently, to further increase the potential capacity of DNA-based data storage systems, the combinatorial composite DNA synthesis method was suggested. This…

In this article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring $\mathcal{R}= \mathbb{F}_{p^m}[v]/\langle v^3 =v \rangle$ where $p$ is an odd prime and $m \geq 1$. In order to…

This paper introduces the use of cable dynamics models as a means to explore the mechanics of DNA on long-length scales. It is on these length scales that DNA forms twisted and curved three-dimensional shapes known as supercoils and loops.…

Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (i.e. rarely accessed), has motivated research for alternative systems of data storage. Because of its biochemical characteristics,…

The present paper is devoted to the study of the combinatorics of 216 maximal $C^3$ circular codes --- a particular type of structure arising in the analysis of genomic sequences. Their circularity property is believed to be intimately…

In this paper, we mainly study the theory of linear codes over the ring $R =\mathbb{Z}_4+u\mathbb{Z}_4+v\mathbb{Z}_4+uv\mathbb{Z}_4$. By the Chinese Remainder Theorem, we have $R$ is isomorphic to the direct sum of four rings…

DNA is an attractive medium for digital data storage. When data is stored on DNA, errors occur, which makes error-correcting coding techniques critical for reliable DNA data storage. To reduce the errors, a common technique is to include…

The yearly global production of data is growing exponentially, outpacing the capacity of existing storage media, such as tape and disk, and surpassing our ability to store it. DNA storage - the representation of arbitrary information as…

Next-generation sequencing technologies provide a revolutionary tool for generating gene expression data. Starting with a fixed RNA sample, they construct a library of millions of differentially abundant short sequence tags or "reads",…

The paper considers coding schemes derived from Reed-Muller (RM) codes, for transmission over input-constrained memoryless channels. Our focus is on the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of…

In this article we count the number of generalized Reed-Solomon (GRS) codes of dimension k and length n, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of…

Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to…

Transcription factor proteins bind specific DNA sequences to control the expression of genes. They contain DNA binding domains which belong to several super-families, each with a specific mechanism of DNA binding. The total number of…

This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…

Minuscule molecular forces can transform DNA into a structure that is elongated by more than half its original length. We demonstrate that this pronounced conformational transition is of relevance to ongoing experimental and theoretical…

Let $q$ be a prime power and let $\mathcal{R}=\mathbb{F}_{q}[u_1,u_2, \cdots, u_k]/\langle f_i(u_i),u_iu_j-u_ju_i\rangle$ be a finite non-chain ring, where $f_i(u_i), 1\leq i \leq k$ are polynomials, not all linear, which split into…