97 citations · 178 across the 29 of their papers we have counts for
21 papers · 1 filter
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…
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…
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.
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…
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…
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…
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…
Homogeneous Weights and Möbius Functions on Finite Rings
Yun Fan, Hongwei Liu
The homogeneous weights and the Möbius functions and Euler phi-functions on finite rings are discussed; some computational formulas for these functions on finite principal ideal ri…
Homogeneous Weights of Matrix Product Codes over Finite Principal Ideal Rings
Yun Fan, San Ling, Hongwei Liu
In this paper, the homogeneous weights of matrix product codes over finite principal ideal rings are studied and a lower bound for the minimum homogeneous weights of such matrix pr…
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…
Cumulative Distance Enumerators of Random Codes and their Thresholds
Yun Fan, San Ling, Hongwei Liu +2
Cumulative weight enumerators of random linear codes are introduced, their asymptotic properties are studied, and very sharp thresholds are exhibited; as a consequence, it is shown…
Self-dual Permutation Codes of Finite Groups in Semisimple Case
Yun Fan, Guanghui Zhang
The existence and construction of self-dual codes in a permutation module of a finite group for the semisimple case are described from two aspects, one is from the point of view of…