Related papers: A Database of $\mathbb{Z}_4$ Codes
In this work it is shown that 20 canonical amino acids (AAs) within genetic code appear to be a whole system with strict distinction in Genetic Code Table (GCT) into some different quantums: 20, 23, 61 amino acid molecules. These molecules…
There has been an increase of interest in code search using natural language. Assessing the performance of such code search models can be difficult without a readily available evaluation suite. In this paper, we present an evaluation…
In a recent paper, Tang and Ding introduced a class of binary cyclic codes of rate close to one half with a designed lower bound on their minimum distance. The definition involves the base $2$ expansion of the integers in their defining…
We consider a new family of codes, termed asymmetric Lee distance codes, that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a…
Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") are described. The degeneracy of the vertebrate mitochondria genetic code is reflected in…
Guess & Check (GC) codes are systematic binary codes that can correct multiple deletions, with high probability. GC codes have logarithmic redundancy in the length of the message $k$, and the encoding and decoding algorithms of these codes…
Optimization methods are essential in solving complex problems across various domains. In this research paper, we introduce a novel optimization method called Gaussian Crunching Search (GCS). Inspired by the behaviour of particles in a…
A code ${\cal C}$ is $\Z_2\Z_4$-additive if the set of coordinates can be partitioned into two subsets $X$ and $Y$ such that the punctured code of ${\cal C}$ by deleting the coordinates outside $X$ (respectively, $Y$) is a binary linear…
Degeneracy is a salient feature of genetic codes, because there are more codons than amino acids. The conventional table for genetic codes suffers from an inability of illustrating a symmetrical nature among genetic base codes. In fact,…
In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…
Based on the generic construction of linear codes, we construct linear codes over the ring $\Bbb Z_4$ via posets of the disjoint union of two chains. We determine the Lee weight distributions of the quaternary codes. Moreover, we obtain…
Over the past 40 years, database management systems (DBMSs) have evolved to provide a sophisticated variety of data management capabilities. At the same time, tools for managing queries over the data have remained relatively primitive. One…
MDS self-dual codes have nice algebraic structures and are uniquely determined by lengths. Recently, the construction of MDS self-dual codes of new lengths has become an important and hot issue in coding theory. In this paper, we develop…
One of the main problems of subspace coding asks for the maximum possible cardinality of a subspace code with minimum distance at least $d$ over $\mathbb{F}_q^n$, where the dimensions of the codewords, which are vector spaces, are contained…
Database search has wide applications and is used as a subroutine in many important algorithms. We shall consider a database with one target item. Quantum algorithm finds the target item in a database faster than any classical algorithm. It…
Progress is being made in code discoverability and preservation, but as discussed at ADASS XXI, many codes still remain hidden from public view. With the Astrophysics Source Code Library (ASCL) now indexed by the SAO/NASA Astrophysics Data…
Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…
In general, we can not use algebraic or enumerative methods to optimize a quality control (QC) procedure so as to detect the critical random and systematic analytical errors with stated probabilities, while the probability for false…
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…
Three algorithms looking for pretty large partial Hadamard matrices are described. Here "large" means that hopefully about a third of a Hadamard matrix (which is the best asymptotic result known so far, [dLa00]) is achieved. The first one…