Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Air Force Engineering University

Combinational Construction of Self-orthogonal Codes and Its Application

Jian Liu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Quantum error-correcting codes protect quantum information against undesirable noise in quantum computation and quantum communication.It is one of important problems that constructing very good quantum codes.There are two methods that use binary codes to construct quantum codes,one is CSS construction,another is Steane construction.These two methods are all based on the construction of binary self-orthogonal codes.Combinational construction of binary self-orthogonal codes is investigated in this paper.From known codes chains of binary self-orthogonal codes and their dual codes chains with given dual distance,new binary self-orthogonal codes of dual distance three,four,five and six are constructed.Based on these results,for each satisfying,S-chains with parameters and are constructed.According to Steane's construction,many very good quantum codes of distance five and six are constructed by the obtained S-chains,some of these quantum codes are new and some of these quantum codes have improved parameters than previously known codes.

Related papers

Quaternary Self-orthogonal Code Chains and Construction of Quantum Error-correcting Codes

Youqian Feng

The method of constructing quantum error-correcting code by the quaternary self-orthogonal sub-code chains and L-chains are investigated in this paper.Random searching method is used to find quaternary self-orthogonal codes and these self-orthogonal codes could form some self-orthogonal code chains.By using combinatorial method,quantum error-correcting codes are constructed in light of L-chains which are constructed by dual of these self-orthogonal codes.The code chains of these self-orthogonal sub-codes and the L-chains which are obtained from the dual of these self-orthogonal sub-codes of length n between 20 and 36 and n=40,45,50,55,60 and dual distance five and six are determined.Some quantum codes of distance five and six are constructed by the obtained L-chains,some quantum error-correcting codes are new.

Journal of Air Force Engineering University•Jan 1, 2008•0 citations

Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication

Yansheng Wu, Yoonjin Lee

It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n≥7. We also find some (almost) “optimal” quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.

Mathematics•Sep 3, 2020•8 citations

Binary Generalized Quasi-Cyclic Self-orthogonal Codes and Binary Construction of Pure Quantum Codes

Weiliang Wang, Yangyu Fan, Luobin Guo

In this paper, a special subclass of binary generalized quasi-cyclic self-orthogonal codes and quantum codes constructed by Steane construction are discussed.Firstly, eight 16-dimensional even length generalized quasi-cyclic self-orthogonal codes with dual distance five are built based on circulant or partial circulant matrices.Secondly, pairs of nested self-orthogonal codes with dual distance five and three are designed by applying an algorithm for searching subcodes of a given code.Thirdly, revised pairs of codes with dual distance six and four are constructed by extending previous pairs of codes, and then eight quantum codes with distance six are obtained by Steane construction.These eight quantum codes are new binary construction by Steane construction and are best known ones.

Advances in intelligent systems research/Advances in Intelligent Systems Research•Jan 1, 2014•1 citation

Subcodes of binary self-dual codes of minimum distance six

Xuejun Zhao

The subcodes of binary self-dual codes whose length n between 22 and 30 and minimum distance six are studied by using of a random search algorithm,and the subcodes of dual distance 3,4,5 and 6 of these self-dual codes are constructed.The code chains of these self-orthogonal subcodes and the S-chains obtained from the dual of these self-orthogonal subcodes are also determined.According to Steane’s construction,some very good quantum codes of distance five and six are constructed by the obtained S-chains,and some of these quantum codes have improved parameters than previously known codes.

Computer Engineering and Applications Journal•Jan 1, 2008•0 citations

Construction of S-chains from maximal self-orthogonal codes

LI Rui-hu

In this paper,the subcodes of the binary maximal self-orthogonal codes whose length n between 11 and 19 are studied.The subcodes with optimal dual distance(or near optimal dual distance) of all indecompose maximal self-orthogonal codes are constructed by combinational method.Consequently,S-chains are constructed from these subcodes with optimal dual distance (or near optimal dual distance).And some very good quantum error-correcting codes are constructed from the S-chains obtained.

Computer Engineering and Applications Journal•Jan 1, 2007•0 citations

Construction of S-chains From Self-dual Codes

Qiu Dang-qing

It is a central problem in the research of coding to study the existence,structure and construction of the certain optimal property codes.In order to construct the quantum error-correcting codes,people have begun to study the self-orthogonal code that has the special self-dual distance.In this paper,two classes of sub-codes,which have optimal dual distance or intended optimal dual distance,of the binary non-decomposable self-dual codes of length n between 12 and 20,such as B12,D14,E16,F16,H18,I18,J20,K20,L20,M20 and S20,and the corresponding S-chain construction are studied.Based on the generator matrices of the self-dual codes,optimal sub-codes of dual distance 2,3 and 4 of these self-dual codes are constructed by using a combinational method.Then code chains of these optimal sub-codes and their dual codes are discussed.Consequently,S-chains are constructed from these sub-codes with optimal dual distance or intended optimal dual distance.Finally,some very good quantum error-correcting codes are constructed from the S-chains obtained.These quantum codes are the ones that the distance reaches the maximum when their n and k are given.

Journal of Air Force Engineering University•Jan 1, 2008•0 citations
Quantum error-correcting codes protect quantum information against undesirable noise in quantum computation and quantum communication.It is one of important problems that constructing very good quantum codes.There are two methods that use binary codes to construct quantum codes,one is CSS construction,another is Steane construction.These two methods are all based on the construction of binary self-orthogonal codes.Combinational construction of binary self-orthogonal codes is investigated in this paper.From known codes chains of binary self-orthogonal codes and their dual codes chains with given dual distance,new binary self-orthogonal codes of dual distance three,four,five and six are constructed.Based on these results,for each satisfying,S-chains with parameters and are constructed.According to Steane's construction,many very good quantum codes of distance five and six are constructed by the obtained S-chains,some of these quantum codes are new and some of these quantum codes have improved parameters than previously known codes.
The method of constructing quantum error-correcting code by the quaternary self-orthogonal sub-code chains and L-chains are investigated in this paper.Random searching method is used to find quaternary self-orthogonal codes and these self-orthogonal codes could form some self-orthogonal code chains.By using combinatorial method,quantum error-correcting codes are constructed in light of L-chains which are constructed by dual of these self-orthogonal codes.The code chains of these self-orthogonal sub-codes and the L-chains which are obtained from the dual of these self-orthogonal sub-codes of length n between 20 and 36 and n=40,45,50,55,60 and dual distance five and six are determined.Some quantum codes of distance five and six are constructed by the obtained L-chains,some quantum error-correcting codes are new.
It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n≥7. We also find some (almost) “optimal” quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.
In this paper, a special subclass of binary generalized quasi-cyclic self-orthogonal codes and quantum codes constructed by Steane construction are discussed.Firstly, eight 16-dimensional even length generalized quasi-cyclic self-orthogonal codes with dual distance five are built based on circulant or partial circulant matrices.Secondly, pairs of nested self-orthogonal codes with dual distance five and three are designed by applying an algorithm for searching subcodes of a given code.Thirdly, revised pairs of codes with dual distance six and four are constructed by extending previous pairs of codes, and then eight quantum codes with distance six are obtained by Steane construction.These eight quantum codes are new binary construction by Steane construction and are best known ones.
The subcodes of binary self-dual codes whose length n between 22 and 30 and minimum distance six are studied by using of a random search algorithm,and the subcodes of dual distance 3,4,5 and 6 of these self-dual codes are constructed.The code chains of these self-orthogonal subcodes and the S-chains obtained from the dual of these self-orthogonal subcodes are also determined.According to Steane’s construction,some very good quantum codes of distance five and six are constructed by the obtained S-chains,and some of these quantum codes have improved parameters than previously known codes.
It is a central problem in the research of coding to study the existence,structure and construction of the certain optimal property codes.In order to construct the quantum error-correcting codes,people have begun to study the self-orthogonal code that has the special self-dual distance.In this paper,two classes of sub-codes,which have optimal dual distance or intended optimal dual distance,of the binary non-decomposable self-dual codes of length n between 12 and 20,such as B12,D14,E16,F16,H18,I18,J20,K20,L20,M20 and S20,and the corresponding S-chain construction are studied.Based on the generator matrices of the self-dual codes,optimal sub-codes of dual distance 2,3 and 4 of these self-dual codes are constructed by using a combinational method.Then code chains of these optimal sub-codes and their dual codes are discussed.Consequently,S-chains are constructed from these sub-codes with optimal dual distance or intended optimal dual distance.Finally,some very good quantum error-correcting codes are constructed from the S-chains obtained.These quantum codes are the ones that the distance reaches the maximum when their n and k are given.