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 Northwest University

Self-orthogonal caps in PG(k-1,4) and construction quantum codes

Youqian Feng

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Aim To investigate the method of constructing quantum error-correcting code by self-orthogonal cap over PG(k-1,4).Methods Using random searching method to find self-orthogonal caps,and using combinatorial method to construct self-orthogonal codes and quantum error-correcting codes.Results A random searching algorithm for complete cap over PG(k-1,4) is designed,and some complete and self-orthogonal caps over PG(k-1,4) are found.By using of these self-orthogonal caps,nine new self-orthogonal codes of dual distance 4 are obtained.Conclusion Some good self-orthogonal codes over F4 and good quantum error-correcting codes are constructed,these codes are better than the previously known.

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

Quantum Codes Constructed by Quantum Caps in PG (4, 5)

Chaofeng Guan, Ruihu Li, Husheng Li +4 more

Abstract In this paper, 57 quantum caps in PG (4,5) are found using a computer-supported search method, and related quantum error-correcting codes are constructed via CSS construction. By comparison, most of these codes have good parameters, and some of them enhance the existing results.

Journal of Physics Conference Series•Jun 1, 2021•0 citations

New Quantum Codes Constructed by Quantum Caps in PG(3,9) and PG(4,9)

Husheng Li, Ruihu Li, Qiang Fu

In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps in$PG(3,9)$and$PG(4,9)$are constructively proven to exist. Then, according to the theorem that each quantum cap corresponds to a quantum error-correcting code with$d=4$, we obtain 278 quantum error-correcting codes. Most of these results break the GV bound, and a number of them are optimal quantum codes or have improved parameters.

IEEE Access•Jan 1, 2020•4 citations

On shortening construction of self-orthogonal quaternary codes

Luobin Guo, Qiang Fu, Ruihu Li +1 more

For a given quaternary self-orthogonal (SO) code, using information of weights of codewords in the dual of the binary code generated by the supports of this SO code, one can construct new quaternary SO code by shortening method. Two methods of determining weights of codewords in the dual of the binary support code of a given large length SO code are presented. Using these methods, we construct many SO codes from a quantum 286-cap in PG(6, 4), and deduce existence of many quantum caps in PG(6, 4) and good quantum codes of distance 4.

International Workshop on Signal Design and its Applications in Communications•Sep 1, 2015•1 citation

Some Quantum Error-Correcting Codes with d = 5

Husheng Li, Ruihu Li, Yu Yao +1 more

Abstract In this paper, we firstly give a computer-support method of searching for Hermitian self-orthogonal linear code. Then two linear codes with dual distance 5 over field F q2 for q = 2,3, respectively, are chosen as ingredients. By use of this searching method, we totally find 88 Hermitian self-orthogonal linear codes and construct 88 related quantum error-correcting codes with d = 5 . Most of these results are best known quantum codes and a number of them have better parameters than that of previous quantum codes.

Journal of Physics Conference Series•Nov 1, 2020•3 citations

Combinational Construction of Self-orthogonal Codes and Its Application

Jian Liu

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.

Journal of Air Force Engineering University•Jan 1, 2009•0 citations
Aim To investigate the method of constructing quantum error-correcting code by self-orthogonal cap over PG(k-1,4).Methods Using random searching method to find self-orthogonal caps,and using combinatorial method to construct self-orthogonal codes and quantum error-correcting codes.Results A random searching algorithm for complete cap over PG(k-1,4) is designed,and some complete and self-orthogonal caps over PG(k-1,4) are found.By using of these self-orthogonal caps,nine new self-orthogonal codes of dual distance 4 are obtained.Conclusion Some good self-orthogonal codes over F4 and good quantum error-correcting codes are constructed,these codes are better than the previously known.
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.
In this paper, we present a computer-supported method of searching for quantum caps. By means of this method and relevant knowledge of combinatorics, many quantum caps inPG(3,9)PG(3,9)PG(3,9)andPG(4,9)PG(4,9)PG(4,9)are constructively proven to exist. Then, according to the theorem that each quantum cap corresponds to a quantum error-correcting code withd=4d=4d=4, we obtain 278 quantum error-correcting codes. Most of these results break the GV bound, and a number of them are optimal quantum codes or have improved parameters.
For a given quaternary self-orthogonal (SO) code, using information of weights of codewords in the dual of the binary code generated by the supports of this SO code, one can construct new quaternary SO code by shortening method. Two methods of determining weights of codewords in the dual of the binary support code of a given large length SO code are presented. Using these methods, we construct many SO codes from a quantum 286-cap in PG(6, 4), and deduce existence of many quantum caps in PG(6, 4) and good quantum codes of distance 4.
Abstract In this paper, we firstly give a computer-support method of searching for Hermitian self-orthogonal linear code. Then two linear codes with dual distance 5 over field F q2 for q = 2,3, respectively, are chosen as ingredients. By use of this searching method, we totally find 88 Hermitian self-orthogonal linear codes and construct 88 related quantum error-correcting codes with d = 5 . Most of these results are best known quantum codes and a number of them have better parameters than that of previous quantum codes.
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.