10 research outputs found
Classification of optimal quaternary Hermitian LCD codes of dimension
Hermitian linear complementary dual codes are linear codes whose intersection
with their Hermitian dual code is trivial. The largest minimum weight among
quaternary Hermitian linear complementary dual codes of dimension is known
for each length. We give the complete classification of optimal quaternary
Hermitian linear complementary dual codes of dimension
Classification of optimal quaternary Hermitian LCD codes of dimension 2
Hermitian linear complementary dual codes are linear codes whose intersections with their Hermitian dual codes are trivial. The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension
An open problem and a conjecture on binary linear complementary pairs of codes
The existence of -ary linear complementary pairs (LCPs) of codes with has been completely characterized so far. This paper gives a
characterization for the existence of binary LCPs of codes. As a result, we
solve an open problem proposed by Carlet (IEEE Trans. Inf. Theory
65(3): 1694-1704, 2019) and a conjecture proposed by Choi (Cryptogr.
Commun. 15(2): 469-486, 2023)
Characterization and mass formulas of symplectic self-orthogonal and LCD codes and their application
The object of this paper is to study two very important classes of codes in
coding theory, namely self-orthogonal (SO) and linear complementary dual (LCD)
codes under the symplectic inner product, involving characterization,
constructions, and their application. Using such a characterization, we
determine the mass formulas of symplectic SO and LCD codes by considering the
action of the symplectic group, and further obtain some asymptotic results.
Finally, under the Hamming distance, we obtain some symplectic SO (resp. LCD)
codes with improved parameters directly compared with Euclidean SO (resp. LCD)
codes. Under the symplectic distance, we obtain some additive SO (resp.
additive complementary dual) codes with improved parameters directly compared
with Hermitian SO (resp. LCD) codes. Further, we also construct many good
additive codes outperform the best-known linear codes in Grassl's code table.
As an application, we construct a number of record-breaking
(entanglement-assisted) quantum error-correcting codes, which improve Grassl's
code table