[BOOK][B] Concise encyclopedia of coding theory
Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …
Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
We prove that the known formulae for computing the optimal number of maximally entangled
pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over …
pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over …
On the hull-variation problem of equivalent linear codes
H Chen - IEEE Transactions on Information Theory, 2023 - ieeexplore.ieee.org
The intersection () of a linear code and its Euclidean dual (Hermitian dual) is called the
Euclidean (Hermitian) hull of this code. It is natural to consider the hull-variation problem …
Euclidean (Hermitian) hull of this code. It is natural to consider the hull-variation problem …
[HTML][HTML] New entanglement-assisted quantum codes from k-Galois dual codes
X Liu, L Yu, P Hu - Finite Fields and Their Applications, 2019 - Elsevier
Entanglement-assisted quantum error-correcting (EAQEC, for short) codes use pre-existing
entanglements between the sender and receiver to boost the rate of transmission. It is …
entanglements between the sender and receiver to boost the rate of transmission. It is …
Construction of MDS twisted Reed–Solomon codes and LCD MDS codes
H Liu, S Liu - Designs, Codes and Cryptography, 2021 - Springer
Maximum distance separable (MDS) codes are optimal in the sense that the minimum
distance cannot be improved for a given length and code size. Twisted Reed–Solomon …
distance cannot be improved for a given length and code size. Twisted Reed–Solomon …
A recursive construction for projective Reed-Muller codes
R San-José - IEEE Transactions on Information Theory, 2024 - ieeexplore.ieee.org
We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-
Muller codes and projective Reed-Muller codes in fewer variables. From this construction …
Muller codes and projective Reed-Muller codes in fewer variables. From this construction …
Optimal quaternary Hermitian LCD codes and their related codes
Z Sun, S Huang, S Zhu - Designs, Codes and Cryptography, 2023 - Springer
Linear codes with complementary dual (LCD codes) play an important role in armoring
implementations against side-channel attacks and fault injection attacks. Hermitian LCD …
implementations against side-channel attacks and fault injection attacks. Hermitian LCD …
[HTML][HTML] Subfield subcodes of projective Reed-Muller codes
Explicit bases for the subfield subcodes of projective Reed-Muller codes over the projective
plane and their duals are obtained. In particular, we provide a formula for the dimension of …
plane and their duals are obtained. In particular, we provide a formula for the dimension of …
Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed–Solomon codes
We study the subfield subcodes of projective Reed–Solomon codes and their duals: we
provide bases for these codes and estimate their parameters. With this knowledge, we can …
provide bases for these codes and estimate their parameters. With this knowledge, we can …
[HTML][HTML] Further results on Euclidean and Hermitian linear complementary dual codes
Z Liu, J Wang - Finite Fields and Their Applications, 2019 - Elsevier
By using the cogredience theories of an alternate matrix, a symmetric matrix and a Hermitian-
symmetric matrix, we will find a special family of generator matrices for any linear code, and …
symmetric matrix, we will find a special family of generator matrices for any linear code, and …