scholarly journals A minimum distance bound for quasi-nD-cyclic codes

2016 ◽  
Vol 41 ◽  
pp. 193-222 ◽  
Author(s):  
Ferruh Özbudak ◽  
Buket Özkaya
Keyword(s):  
Minimum Distance ◽  
Cyclic Codes ◽  
Distance Bound ◽  
Minimum Distance Bound

scholarly journals From Generalization of Bacon-Shor Codes to High Performance Quantum LDPC Codes

2021 ◽  
Author(s):  
Jihao Fan ◽  
Jun Li ◽  
Ya Wang ◽  
Yonghui Li ◽  
Min-Hsiu Hsieh ◽  
...  
Keyword(s):  
Minimum Distance ◽  
High Performance ◽  
Ldpc Codes ◽  
Quantum Error Correction ◽  
Concatenated Codes ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Distance Bound ◽  
Quantum Error ◽  
Minimum Distance Bound

Abstract We utilize a concatenation scheme to construct new families of quantum error correction codes that include the Bacon-Shor codes. We show that our scheme can lead to asymptotically good quantum codes while Bacon-Shor codes cannot. Further, the concatenation scheme allows us to derive quantum LDPC codes of distance Ω(N2/3/loglogN) which can improve Hastings’s recent result [arXiv:2102.10030] by a polylogarithmic factor. Moreover, assisted by the Evra-Kaufman- Zémor distance balancing construction, our concatenation scheme can yield quantum LDPC codes with non-vanishing code rates and better minimum distance upper bound than the hypergraph product quantum LDPC codes. Finally, we derive a family of fast encodable and decodable quan- tum concatenated codes with parameters Q = [[N,Ω(√N),Ω(√N)]] and they also belong to the Bacon-Shor codes. We show that Q can be encoded very efficiently by circuits of size O(N) and depth O(√N), and can correct any adversarial error of weight up to half the minimum distance bound in O(√N) time. To the best of our knowledge, they are the most powerful quantum codes for correcting so many adversarial errors in sublinear time by far.

Use of Grobner bases to decode binary cyclic codes up to the true minimum distance

1994 ◽  
Vol 40 (5) ◽  
pp. 1654-1661 ◽  
Author(s):  
Xuemin Chen ◽  
I.S. Reed ◽  
T. Helleseth ◽  
T.K. Truong
Keyword(s):  
Minimum Distance ◽  
Cyclic Codes ◽  
Gröbner Bases ◽  
Grobner Bases

On some bounds on the minimum distance of cyclic codes over finite fields

2014 ◽  
Vol 76 (2) ◽  
pp. 173-178
Author(s):  
Ferruh Özbudak ◽  
Seher Tutdere ◽  
Oğuz Yayla
Keyword(s):  
Finite Fields ◽  
Minimum Distance ◽  
Cyclic Codes

Optimal p-ary cyclic codes with minimum distance four from monomials

2015 ◽  
Vol 8 (4) ◽  
pp. 541-554 ◽  
Author(s):  
Guangkui Xu ◽  
Xiwang Cao ◽  
Shanding Xu
Keyword(s):  
Minimum Distance ◽  
Cyclic Codes
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