Related papers: Genetic Code as a Harmonic System: three Supplemen…
This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation…
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
The post-genomic era has brought opportunities to bridge traditionally separate fields of early history of life and brought new insight into origin and evolution of biodiversity. According to distributions of codons in genome sequences, I…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
In this paper it is shown that within a Combined Genetic Code Table, realized through a combination of Watson-Crick Table and Codon Path Cube it exists, without an exception, a strict distinction between two classes of enzymes…
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…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…
A quantitative theory on the construction and the evolution of the genetic code is proposed. Through introducing the concept of mutational deterioration (MD) and developing a theoretical formalism on MD minimization we have proved: 1, the…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…
We develop genetic algorithms for searching quantum circuits, in particular stabilizer quantum error correction codes. Quantum codes equivalent to notable examples such as the 5-qubit perfect code, Shor's code, and the 7-qubit color code…
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain…
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…
A quaternionic representation of the genetic code, previously reported by the authors, is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation assigns to each nucleotide base a prime…
Motivation: Millions of genes in the modern species belong to only thousands of `gene families'. A gene family includes instances of the same gene in different species (orthologs) and duplicate genes in the same species (paralogs). Genes…
Information theoretic analysis of genetic languages indicates that the naturally occurring 20 amino acids and the triplet genetic code arose by duplication of 10 amino acids of class-II and a doublet genetic code having codons NNY and…
Genome sequencing is essential to decode genetic information, identify organisms, understand diseases and advance personalized medicine. A critical step in any genome sequencing technique is genome assembly. However, de novo genome…
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum…
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable…