Quantum codes with bounded minimum distance

Emre Kolotoğlu, Mustafa Sarı

Daryus Chandra, Zunaira Babar, Hung Viet Nguyen +4 more

The tradeoff between the quantum coding rate and the associated error correction capability is characterized by the quantum coding bounds. The unique solution for this tradeoff does not exist, but the corresponding lower and the upper bounds can be found in the literature. In this treatise, we survey the existing quantum coding bounds and provide new insights into the classical to quantum duality for the sake of deriving new quantum coding bounds. Moreover, we propose an appealingly simple and invertible analytical approximation, which describes the tradeoff between the quantum coding rate and the minimum distance of quantum stabilizer codes. For example, for a half-rate quantum stabilizer code having a code word length of n = 128, the minimum distance is bounded by 11 <; d <; 22, while our formulation yields a minimum distance of d = 16 for the above-mentioned code. Ultimately, our contributions can be used for the characterization of quantum stabilizer codes.

Taoran Liu, Xiaoshan Kai

Hachiro Fujita

In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of Ashikhmin--Litsyn--Tsfasman and Matsumoto. We also give a polynomial-time decoding algorithm for the codes that can decode up to one fourth of the lower bound on the minimum distance of the codes.

Anonymous, Ashish Kakkar, Anatoly Y. Dymarsky

Matrapu Sumanth Datt, Mansoor Ali, Rubayya +1 more

In this paper, we consider Quasi Cyclic Low Density Parity Check (QC LDPC) codes.This important family of codes has wide applications in the field of information theory and post-quantum cryptography.In [1], the authors consider type-1 QC LDPC codes and give an upper bound on the minimum distance of these codes.Stimulated by their work, in this paper we give upper bound on the minimum distance of type-2 QC LDPC codes.