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Subspace coverings and generalized covering radii of generalized Zetterberg codes
Shitao Li, Yang Li, Gaojun Luo +1
Generalized covering radii measure how many columns of a parity-check matrix are needed to generate several syndromes simultaneously. Their finite-geometric counterparts are $(ρ,t)…
Entanglement-Assisted Quantum Locally Recoverable Codes: Characterizations, Bounds, and Constructions
Yang Li, San Ling, Zhenliang Lu +2
Quantum locally recoverable codes (qLRCs) allow a single qudit erasure to be corrected by accessing only a small number of other qudits. Standard CSS and Hermitian constructions, h…
Improved bounds and optimal constructions of pure quantum locally recoverable codes
Yang Li, Shitao Li, Gaojun Luo +1
By incorporating the concept of locality into quantum information theory, quantum locally recoverable codes (qLRCs) have been proposed, motivated by their potential applications in…
Generalized Repetition Codes and Their Application to HARQ
Chaofeng Guan, Gaojun Luo, Lan Luo +2
The inherent uncertainty of communication channels implies that any coding scheme has a non-zero probability of failing to correct errors, making retransmission mechanisms essentia…
On optimal quantum LRCs from the Hermitian construction and -designs
Yang Li, Shitao Li, Huimin Lao +2
In a recent work, quantum locally recoverable codes (qLRCs) have been introduced for their potential application in large-scale quantum data storage and implication for quantum LDP…
Lower Bounds for Error Coefficients of Griesmer Optimal Linear Codes via Iteration
Chaofeng Guan, Shitao Li, Gaojun Luo +2
The error coefficient of a linear code is defined as the number of minimum-weight codewords. In an additive white Gaussian noise channel, optimal linear codes with the smallest err…
Combinatorial Constructions of Optimal Quaternary Additive Codes
Chaofeng Guan, Jingjie Lv, Gaojun Luo +1
This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight c…
On Linear Codes Whose Hermitian Hulls are MD
Gaojun Luo, Lin Sok, Martianus Frederic Ezerman +1
Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have b…
Griesmer Bound and Constructions of Linear Codes in -Symbol Metric
Gaojun Luo, Martianus Frederic Ezerman, Cem Güneri +2
The -symbol metric is a generalization of the Hamming metric. Linear codes, in the -symbol metric, have been used in the read channel whose outputs consist of consecutive…
Bounds and Constructions of Quantum Locally Recoverable Codes from Quantum CSS Codes
Gaojun Luo, Bocong Chen, Martianus Frederic Ezerman +1
Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have…
Improved Spectral Bound for Quasi-Cyclic Codes
Gaojun Luo, Martianus Frederic Ezerman, San Ling +1
Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes…
On non-expandable cross-bifix-free codes
Chunyan Qin, Bocong Chen, Gaojun Luo
A cross-bifix-free code of length over is defined as a non-empty subset of satisfying that the prefix set of each codeword is disjoint from the…