Related papers: On the optimality of the standard genetic code: th…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We…
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…
Messenger RNA (mRNA) vaccines are being used for COVID-19, but still suffer from the critical issue of mRNA instability and degradation, which is a major obstacle in the storage, distribution, and efficacy of the vaccine. Previous work…
Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter $q$, $0{<}q{<}1$. By encoding pairs of symbols, it is possible to reduce the…
We show an interesting PBD-closure result for the set of lengths of constant-composition codes whose distance and size meet certain conditions. A consequence of this PBD-closure result is that the size of optimal constant-composition codes…
In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…
In [1], the authors proposed a new model of DNA storage system that integrates all three steps of retrieval and introduced the concept of DNA-correcting codes, which guarantees that the output of the storage system can be decoded to the…
The idea of the evolution of the genetic code from the CG to the CGUA alphabet has been developed further. The assumption of the originally triplet structure of the genetic code has been substantiated. The hypothesis of the emergence of…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
Requiring stability of genetic code against translation errors, modelised by suitable mathematical operators in the crystal basis model of the genetic code, the main features of the organisation in multiplets of the mitochondrial and of the…
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
The problem of securing a network coding communication system against an eavesdropper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop…
Network coding is all about combining a variety of packets and forwarding as much packets as possible in each transmission operation. The network coding technique improves the throughput efficiency of multi-hop wireless networks by taking…
Classical population genetics a priori assigns fitness to alleles without considering molecular or functional properties of proteins that these alleles encode. Here we study population dynamics in a model where fitness can be inferred from…
The algebraic structures of the genetic code are most important to obtain additional information about the semantic code and its applications. In this paper we define two dual Boolean codon lattices of the genetic code using hydrogen bond…
Alternative splicing allows an organism to make different proteins in different cells at different times, all from the same gene. In a cell that uses alternative splicing, the total length of all the exons is much shorter than in a cell…
Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The optimization procedure is based on the evolution of…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…