5 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
Optimal Quaternary Hermitian Linear Complementary Dual Codes for Entanglement-Assisted Quantum Error Correction
The objective of this thesis is to find suboptimal and optimal parameters from classical codes and import them into entanglement-assisted quantum codes. The thesis begins by introducing classical error correction, followed by a detailed introduction to quantum computing. Topics that are discussed in the introduction include qubits, quantum phenomena, such as superposition and entanglement, and quantum gates/circuits. The thesis then reviews the basics of quantum error correction and provides Shor's code to reinforce the reader's understanding. Subsequently, the formalism of stabilizer codes is thoroughly examined. We then explain the generalized concept of stabilizer codes which is entanglement-assisted quantum codes. They do not require generators to satisfy the commutativity property. Rather, they utilize the usage of ebits to resolve the anti-commutativity constraint. Next, the thesis explains quaternary field and then the Java program implemented to find the optimal parameters. Lastly, the thesis concludes with presenting the parameters of the new codes that were obtained throughout the research. We have found the suboptimal largest distance for quaternary hermitian linear complementary dual codes that can be imported as entanglement-assisted quantum error correction for parameters [22, 9, 9 or 10]β, [22, 12, 7 or 8]β, [23, 8, 11 or 12]β, [23, 10, 9 or 10]β, [23, 13, 7 or 8]β, [24, 10, 10 or 11]β, [24, 11, 9 or 10]β, [24, 14, 7 or 8]β, [25, 12, 9 or 10]β, [25, 13, 8 or 9]β, as well as the optimal largest distance for [17, 11, 5]β and [17, 13, 3]β
The hull of two classical propagation rules and their applications
Propagation rules are of great help in constructing good linear codes. Both
Euclidean and Hermitian hulls of linear codes perform an important part in
coding theory. In this paper, we consider these two aspects together and
determine the dimensions of Euclidean and Hermitian hulls of two classical
propagation rules, namely, the direct sum construction and the
-construction. Some new criteria for resulting codes
derived from these two propagation rules being self-dual, self-orthogonal or
linear complement dual (LCD) codes are given. As applications, we construct
some linear codes with prescribed hull dimensions and many new binary, ternary
Euclidean formally self-dual (FSD) LCD codes, quaternary Hermitian FSD LCD
codes and good quaternary Hermitian LCD codes which are optimal or have best or
almost best known parameters according to Datebase at
. Moreover, our methods contributes positively to
improve the lower bounds on the minimum distance of known LCD codes.Comment: 16 pages, 5 table