Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into...Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.展开更多
IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub&g...IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub>i</sub>p<sup>i</sup>（1-p）<sup>n-1</sup>, （1）where （A<sub>0</sub>, A<sub>1</sub>,…, A<sub>n</sub>） is the weight distribution of C. If for all 0≤p≤0.5, P<sub>e</sub>（p）≤P<sub>e</sub>（0. 5） = 2<sup>k-n</sup>-2<sup>-n</sup>, then C is called good for error detection. Moreover, if P<sub>e</sub> （p） ismonotonously increasing in the interval [0, 0.5], then C is called proper. Clearly, propercodes are good.展开更多
A combinatorial batch code has strong practical motivation in the distributed storage and retrieval of data in a database.In this survey,we give a brief introduction to the combinatorial batch codes and some progress.
The undetected error probability and error detection capability of shortened Hamming codes and their dual codes are studied in this paper. We also obtain some interesting properties for the shortened Simplex codes.
文摘Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.
文摘IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub>i</sub>p<sup>i</sup>（1-p）<sup>n-1</sup>, （1）where （A<sub>0</sub>, A<sub>1</sub>,…, A<sub>n</sub>） is the weight distribution of C. If for all 0≤p≤0.5, P<sub>e</sub>（p）≤P<sub>e</sub>（0. 5） = 2<sup>k-n</sup>-2<sup>-n</sup>, then C is called good for error detection. Moreover, if P<sub>e</sub> （p） ismonotonously increasing in the interval [0, 0.5], then C is called proper. Clearly, propercodes are good.
文摘A combinatorial batch code has strong practical motivation in the distributed storage and retrieval of data in a database.In this survey,we give a brief introduction to the combinatorial batch codes and some progress.
基金supported by the National Natural Science Foundation of China, No. 69802008.
文摘The undetected error probability and error detection capability of shortened Hamming codes and their dual codes are studied in this paper. We also obtain some interesting properties for the shortened Simplex codes.
