97 citations · 178 across the 29 of their papers we have counts for
29 papers
Consta-dihedral Codes over Finite Fields
Yun Fan, Yue Leng
It is proved in a reference (Fan, Lin, IEEE TIT, vol.67, pp.5016-5025) that the self-dual (LCD respectively) dihedral codes over a finite field~ with are asymptoticall…
Sharp Uncertainty Principle for Transitive -Sets over Arbitrary Fields and Finite Groups
Bocong Chen, Yun Fan, Gaojun Luo
For any finite group , any transitive -set and any field , we consider the vector space of all functions from to , which is a -spa…
Double Constacyclic Codes over Two Finite Commutative Chain Rings
Yun Fan, Hualu Liu
Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as -additive cyclic codes and quasi-cyclic codes…
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…
Self-dual 2-quasi-cyclic Codes and Dihedral Codes
Yun Fan, Yuchang Zhang
We characterize the structure of 2-quasi-cyclic codes over a finite field F by the so-called Goursat Lemma. With the characterization, we exhibit a necessary and sufficient conditi…
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…
Constacyclic Codes over Commutative Finite Principal Ideal Rings
Yun Fan
For any constacyclic code over a finite commutative chain ring of length coprime to the characteristic of the ring, we construct explicitly generator polynomials and check polynomi…
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…
-Additive Cyclic Codes Are Asymptotically Good
Yun Fan, Hualu Liu
We construct a class of -additive cyclic codes generated by pairs of polynomials, study their algebraic structures, and obtain the generator matrix of any…
Galois LCD Codes over Finite Fields
Xiusheng Liu, Yun Fan, Hualu Liu
In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linea…
Isometrically Self-dual Cyclic Codes
Yun Fan, Liang Zhang
General isometries of cyclic codes, including multipliers and translations, are introduced; and isometrically self-dual cyclic codes are defined. In terms of Type-I duadic splittin…
Permutation-like Matrix Groups with a Maximal Cycle of Length Power of Two
Guodong Deng, Yun Fan
If every element of a matrix group is similar to a permutation matrix, then it is called a permutation-like matrix group. References [4], [5] and [6] showed that, if a permutation-…
Nonlinear functions and difference sets on group actions
Yun Fan, Bangteng Xu
Let , be finite groups and let be a finite -set. -perfect nonlinear functions from to have been studied in several papers. They have more interesting prope…
Double Circulant Matrices
Yun Fan, Hualu Liu
Double circulant matrices are introduced and studied. A formula to compute the rank r of a double circulant matrix is exhibited; and it is shown that any consecutive r rows of the…
Galois Self-Dual Constacyclic Codes
Yun Fan, Liang Zgang
Generalizing Euclidean inner product and Hermitian inner product, we introduce Galois inner products, and study the Galois self-dual constacyclic codes in a very general setting by…
Quasi-cyclic Codes of Index 1.5
Yun Fan, Hualu Liu
We introduce quasi-cyclic codes of index 1.5, construct such codes in terms of polynomials and matrices; and prove that the quasi-cyclic codes of index 1.5 are asymptotically good.
Permutation-like Matrix Groups with a Maximal Cycle of Power of Odd Prime Length
Guodong Deng, Yun Fan
If every element of a matrix group is similar to a permutation matrix, then it is called a permutation-like matrix group. References [4] and [5] showed that, if a permutation-like…
Iso-Orthogonality and Type II Duadic Constacyclic Codes
Yun Fan, Liang Zhang
Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their proper…
Hyperbolic Modules of Finite Group Algebras over Finite Fields of Characteristic Two
Ping Jin, Yun Fan
Let be a finite group and let be a finite field of characteristic . We introduce \emph{-special subgroups} and \emph{-special elements} of . In the case where $…
Polyadic Constacyclic Codes
Bocong Chen, Hai Q. Dinh, Yun Fan +1
For any given positive integer , a necessary and sufficient condition for the existence of Type I -adic constacyclic codes is given. Further, for any given integer , a nec…
Fourier Transforms and Bent Functions on Finite Abelian Group-Acted Sets
Yun Fan, Bangteng Xu
Let be a finite abelian group acting faithfully on a finite set . As a natural generalization of the perfect nonlinearity of Boolean functions, the -bentness and -perf…
Matrix Product Codes over Finite Commutative Frobenius Rings
Yun Fan, San Ling, Hongwei Liu
Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices…
Permutation-like Matrix Groups with a Maximal Cycle of Prime Square Length
Guodong Deng, Yun Fan
A matrix group is said to be permutation-like if any matrix of the group is similar to a permutation matrix. G. Cigler proved that, if a permutation-like matrix group contains a no…
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…