8,526 research outputs found
List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes
A list decoding algorithm for matrix-product codes is provided when are nested linear codes and is a non-singular by columns matrix. We
estimate the probability of getting more than one codeword as output when the
constituent codes are Reed-Solomon codes. We extend this list decoding
algorithm for matrix-product codes with polynomial units, which are
quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for
matrix-product codes with polynomial units
Locally recoverable codes from the matrix-product construction
Matrix-product constructions giving rise to locally recoverable codes are
considered, both the classical and localities. We study the
recovery advantages offered by the constituent codes and also by the defining
matrices of the matrix product codes. Finally, we extend these methods to a
particular variation of matrix-product codes and quasi-cyclic codes.
Singleton-optimal locally recoverable codes and almost Singleton-optimal codes,
with length larger than the finite field size, are obtained, some of them with
superlinear length
Quantum Error Correction beyond the Bounded Distance Decoding Limit
In this paper, we consider quantum error correction over depolarizing
channels with non-binary low-density parity-check codes defined over Galois
field of size . The proposed quantum error correcting codes are based on
the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting
quantum codes outperform the best known quantum codes and surpass the
performance limit of the bounded distance decoder. By increasing the size of
the underlying Galois field, i.e., , the error floors are considerably
improved.Comment: To appear in IEEE Transactions on Information Theor
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