Related papers: Genetic Code: A New Understanding of Codon - Amino…
The famous series of Fibonacci numbers is defined by a recursive equation saying that each number is the sum of its two predecessors, with the initial condition that the first two numbers are equal to unity. Here, we show that the numbers…
In silico design of new molecules and materials with desirable quantum properties by high-throughput screening is a major challenge due to the high dimensionality of chemical space. To facilitate its navigation, we present a unification of…
There has been much research on codes over $\mathbb{Z}_4$, sometimes called quaternary codes, for over a decade. Yet, no database is available for best known quaternary codes. This work introduces a new database for quaternary codes. It…
Essential genes constitute the core of genes which cannot be mutated too much nor lost along the evolutionary history of a species. Natural selection is expected to be stricter on essential genes and on conserved (highly shared) genes, than…
We will describe an algorithm to arrange all the positive and negative integer numbers. This array of numbers permits grouping them in six different Classes, $\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$, and $\zeta$. Particularly,…
DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a…
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12}…
Diatomic molecular codes [arXiv:1911.00099] are designed to encode quantum information in the orientation of a diatomic molecule, allowing error correction from small torques and changes in angular momentum. Here, we directly study noise…
A rigorous thermodynamic expression is derived for the total biological information capacity per unit length of a DNA molecule. The total information includes the usual four letter coding sequence information plus that excess information…
Amino acids in solar system bodies may have played a key role in the chemistry that led to the origin of life on Earth. We present laboratory studies testing the stability of amino acids against gamma radiation photolysis. All the 20 chiral…
Various physical properties such as dipole moment, heat of formation and energy of the most stable formation of nucleotides and bases were calculated by PM3 (modified neglect of diatomic overlap, parametric method number 3) and AM1 (Austin…
Code loops are certain Moufang $2$-loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More precisely, code loops are central extensions of the group of…
Numeral systems across the world's languages vary in fascinating ways, both regarding their synchronic structure and the diachronic processes that determined how they evolved in their current shape. For a proper comparison of numeral…
Despite being used for decades as stabilizers, amino acids (AAs) remain mysterious components of many medical and biological formulations. Hypotheses on their role vary ranging from hydrotropic to protein-specific effects (stabilization…
In this note, we study the classification of $\mathbb{Z}_4$-codes. For some special cases $(k_1,k_2)$, by hand, we give a classification of $\mathbb{Z}_4$-codes of length $n$ and type $4^{k_1}2^{k_2}$ satisfying a certain condition. Our…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
Ultrametric approach to the genetic code and the genome is considered and developed. $p$-Adic degeneracy of the genetic code is pointed out. Ultrametric tree of the codon space is presented. It is shown that codons and amino acids can be…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight…
A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how…
All binary self-dual [44,22,8] codes with an automorphism of order 3 or 7 are classified. In this way we complete the classification of extremal self-dual codes of length 44 having an automorphism of odd prime order.