97 citations · 108 across the 12 of their papers we have counts for
12 papers
Asymptotic Properties of Quasi-Group Codes
Yun Fan, Liren Lin
This is a manuscript of a chapter prepared for a book. The good codes possess large information length and large minimum distance. A class of codes is said to be asymptotically goo…
A new locally linear embedding scheme in light of Hessian eigenmap
Liren Lin, Chih-Wei Chen
We provide a new interpretation of Hessian locally linear embedding (HLLE), revealing that it is essentially a variant way to implement the same idea of locally linear embedding (L…
Avoiding unwanted results in locally linear embedding: A new understanding of regularization
Liren Lin
We demonstrate that locally linear embedding (LLE) inherently admits some unwanted results when no regularization is used, even for cases in which regularization is not supposed to…
Self-dual -quasi-abelian Codes
Liren Lin, Yun Fan
A kind of self-dual quasi-abelian codes of index over any finite field is introduced. By counting the number of such codes and the number of the codes of this kind whose re…
Dihedral group codes over finite fields
Yun Fan, Liren Lin
Bazzi and Mitter [3] showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with good mathemati…
Constacyclic symbol-pair codes: lower bounds and optimal constructions
Bocong Chen, Liren Lin, Hongwei Liu
Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pa…
Three new classes of optimal frequency-hopping sequence sets
Bocong Chen, Liren Lin, San Ling +1
The study of frequency-hopping sequences (FHSs) has been focused on the establishment of theoretical bounds for the parameters of FHSs as well as on the construction of optimal FHS…
Mixed dimensional infinite soliton trains for nonlinear Schrödinger equations
Liren Lin, Tai-Peng Tsai
In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schrödinger equations whose asymptotic profiles at time infinity consist of in…
Thresholds of Random Quasi-Abelian Codes
Yun Fan, Liren Lin
For a random quasi-abelian code of rate , it is shown that the GV-bound is a threshold point: if is less than the GV-bound at , then the probability of the relative dista…
Phase transition between two-component and three-component ground states of spin-1 Bose-Einstein condensates
Liren Lin, I-Liang Chern
For an antiferromagnetic spin-1 Bose-Einstein condensate under an applied uniform magnetic field, its ground state undergoes a phase transition from a two-compon…
Constacyclic Codes over Finite Fields
Bocong Chen, Yun Fan, Liren Lin +1
An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length are…
Proofs of some simplified characterizations of the ground states of spin-1 Bose-Einstein condensates
Liren Lin, I-Liang Chern
We justify some characterizations of the ground states of spin-1 Bose-Einstein condensates exhibited from numerical simulations. For ferromagnetic systems, we show the validity of…