Efficient decoding of Reed-Solomon codes beyond half the minimum distance

2002 ◽  
Author(s):  
R.M. Roth ◽  
G. Ruckenstein
Keyword(s):  
Minimum Distance ◽  
Reed Solomon Codes ◽  
Efficient Decoding

Golden codes: quantum LDPC codes from regular tessellations of hyperbolic 4-manifolds

2019 ◽  
Vol 19 (5&6) ◽  
pp. 361-391
Author(s):  
Vivien Londe ◽  
Anthony Leverrier
Keyword(s):  
Local Structure ◽  
Minimum Distance ◽  
Ldpc Codes ◽  
Decoding Algorithm ◽  
Efficient Decoding

We adapt a construction of Guth and Lubotzky \cite{GL14} to obtain a family of quantum LDPC codes with non-vanishing rate and minimum distance scaling like n^{0.1} where n is the number of physical qubits. Similarly as in Ref.~\cite{GL14}, our homological code family stems from hyperbolic 4-manifolds equipped with tessellations. The main novelty of this work is that we consider a regular tessellation consisting of hypercubes. We exploit this strong local structure to design and analyze an efficient decoding algorithm.

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