Yuan Cao

activity

20152023

p^{s} n

over

F_{p^{m}} + u F_{p^{m}}

12 citations · 28 across the 22 of their papers we have counts for

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cs.IT2021

Construction and enumeration of left dihedral codes satisfying certain duality properties

Yuan Cao, Yonglin Cao, Fanghui Ma

Let $F_{q}$ be the finite field of $q$ elements and let $D_{2 n} = ⟨ x, y ∣ x^{n} = 1, y^{2} = 1, y x y = x^{n - 1} ⟩$ be the dihedral group of order $n$ . Left ideals of the gr…

cs.IT2020

An explicit expression for Euclidean self-dual cyclic codes of length $2^{k}$ over Galois ring $GR (4, m)$

Yuan Cao, Yonglin Cao, San ling +1

For any positive integers $m$ and $k$ , existing literature only determines the number of all Euclidean self-dual cyclic codes of length $2^{k}$ over the Galois ring $GR (4, m)$ ,…

cs.IT2019

On self-duality and hulls of cyclic codes over $\frac{F _{2^{m}} [ u ]}{⟨ u ^{k} ⟩}$ with oddly even length

Yonglin Cao, Yuan Cao, Fang-Wei Fu

Let $F_{2^{m}}$ be a finite field of $2^{m}$ elements, and $R = F_{2^{m}} [u] / ⟨ u^{k} ⟩ = F_{2^{m}} + u F_{2^{m}} + \dots + u^{k - 1} F_{2^{m}}$ ($u^k=0…

cs.IT2019★ 4 cited

Construction and enumeration for self-dual cyclic codes of even length over $F_{2^{m}} + u F_{2^{m}}$

Yuan Cao, Yonglin Cao, Hai Q. Dinh +2

Let $F_{2^{m}}$ be a finite field of cardinality $2^{m}$ , $R = F_{2^{m}} + u F_{2^{m}}$ $(u^{2} = 0)$ and $s, n$ be positive integers such that $n$ is odd. In this paper,…

cs.IT2019

An efficient method to construct self-dual cyclic codes of length $p^{s}$ over $F_{p^{m}} + u F_{p^{m}}$

Yuan Cao, Yonglin Cao, Hai Q. Dinh +1

Let $p$ be an odd prime number, $F_{p^{m}}$ be a finite field of cardinality $p^{m}$ and $s$ a positive integer. Using some combinatorial identities, we obtain certain propert…

cs.IT2019

Explicit representation for a class of Type 2 constacyclic codes over the ring $F_{2^{m}} [u] / ⟨ u^{2 λ} ⟩$ with even length

Yuan Cao, Yonglin Cao, Hai Q. Dinh +2

Let $F_{2^{m}}$ be a finite field of cardinality $2^{m}$ , $λ$ and $k$ be integers satisfying $λ, k \geq 2$ and denote $R = F_{2^{m}} [u] / ⟨ u^{2 λ} ⟩$ . Let $δ,α\in…

cs.IT2019

Self-dual binary $[8 m, 4 m]$ -codes constructed by left ideals of the dihedral group algebra $F_{2} [D_{8 m}]$

Yuan Cao, Yonglin Cao, Fang-Wei Fu +1

Let $m$ be an arbitrary positive integer and $D_{8 m}$ be a dihedral group of order $8 m$ , i.e., $D_{8 m} = ⟨ x, y ∣ x^{4 m} = 1, y^{2} = 1, y x y = x^{- 1} ⟩$ . Left ideals of the dihed…

cs.IT2018★ 3 cited

An explicit representation and enumeration for self-dual cyclic codes over $F_{2^{m}} + u F_{2^{m}}$ of length $2^{s}$

Yuan Cao, Yonglin Cao, Hai Q. Dinh +1

Let $F_{2^{m}}$ be a finite field of cardinality $2^{m}$ and $s$ a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations ov…

cs.IT2018

An explicit representation and enumeration for negacyclic codes of length $2^{k} n$ over $Z_{4} + u Z_{4}$

Yonglin Cao, Yuan Cao, Rama Krishna Bandi +1

In this paper, an explicit representation and enumeration for negacyclic codes of length $2^{k} n$ over the local non-principal ideal ring $R = Z_{4} + u Z_{4}$ $(u^{2} = 0)$ is…

cs.IT2018★ 3 cited

A class of repeated-root constacyclic codes over $F_{p^{m}} [u] / ⟨ u^{e} ⟩$ of Type $2$

Yuan Cao, Yonglin Cao, Hai Q. Dinh +3

Let $F_{p^{m}}$ be a finite field of cardinality $p^{m}$ where $p$ is an odd prime, $n$ be a positive integer satisfying $gcd (n, p) = 1$ , and denote $R=\mathbb{F}_{p^m}[u]/…

cs.IT2018

Matrix-product structure of constacyclic codes over finite chain rings $F_{p^{m}} [u] / ⟨ u^{e} ⟩$

Yuan Cao, Yonglin Cao, Fang-Wei Fu

Let $m, e$ be positive integers, $p$ a prime number, $F_{p^{m}}$ be a finite field of $p^{m}$ elements and $R = F_{p^{m}} [u] / ⟨ u^{e} ⟩$ which is a finite chain ri…

cs.IT2018★ 2 cited

Negacyclic codes over the local ring $Z_{4} [v] / ⟨ v^{2} + 2 v ⟩$ of oddly even length and their Gray images

Yuan Cao, Yonglin Cao

Let $R = Z_{4} [v] / ⟨ v^{2} + 2 v ⟩ = Z_{4} + v Z_{4}$ ( $v^{2} = 2 v$ ) and $n$ be an odd positive integer. Then $R$ is a local non-principal ideal ring of $16$ e…

cs.IT2017★ 1 cited

Complete classification for simple root cyclic codes over local rings $Z_{p^{s}} [v] / ⟨ v^{2} - p v ⟩$

Yuan Cao, Yonglin Cao

Let $p$ be a prime integer, $n, s \geq 2$ be integers satisfying $gcd (p, n) = 1$ , and denote $R = Z_{p^{s}} [v] / ⟨ v^{2} - p v ⟩$ . Then $R$ is a local non-principal ideal…

cs.IT2017★ 2 cited

Matrix-product structure of repeated-root constacyclic codes over finite fields

Yuan Cao, Yonglin Cao, Fang-Wei Fu

For any prime number $p$ , positive integers $m, k, n$ satisfying $gcd (p, n) = 1$ and $λ_{0} \in F_{p^{m}}^{\times}$ , we prove that any $λ_{0}^{p^{k}}$ -constacyclic code of length…

cs.IT2017

On a class of constacyclic codes over the non-principal ideal ring $Z_{p^{s}} + u Z_{p^{s}}$

Yuan Cao, Yonglin Cao

$(1 + pw)$ -constacyclic codes of arbitrary length over the non-principal ideal ring $Z_{p^{s}} + u Z_{p^{s}}$ are studied, where $p$ is a prime, $w\in \mathbb{Z}_{p^s}^{\…

cs.IT2016

The Gray image of constacyclic codes over the finite chain ring $F_{p^{m}} [u] / ⟨ u^{k} ⟩$

Yuan Cao, Yonglin Cao

Let $F_{p^{m}}$ be a finite field of cardinality $p^{m}$ , where $p$ is a prime, and $k, N$ be any positive integers. We denote $R_k=F_{p^m}[u]/\langle u^k\rangle =F_{p^m}+uF_{…

cs.IT2016

Complete classification of $(δ + α u^{2})$ -constacyclic codes over $F_{2^{m}} [u] / ⟨ u^{4} ⟩$ of oddly even length

Yonglin Cao, Yuan Cao

Let $F_{2^{m}}$ be a finite field of cardinality $2^{m}$ , $R = F_{2^{m}} [u] / ⟨ u^{4} ⟩)$ and $n$ is an odd positive integer. For any $δ,α\in \mathbb{F}_{2^m}^{\ti…

cs.IT2016

Left dihedral codes over Galois rings $GR (p^{2}, m)$

Yonglin Cao, Yuan Cao, Fang-Wei Fu

Let $D_{2 n} = ⟨ x, y ∣ x^{n} = 1, y^{2} = 1, y x y = x^{- 1} ⟩$ be a dihedral group, and $R = GR (p^{2}, m)$ be a Galois ring of characteristic $p^{2}$ and cardinality $p^{2 m}$ where $p…

cs.IT2015★ 12 cited

Constacyclic codes of length $p^{s} n$ over $F_{p^{m}} + u F_{p^{m}}$

Yonglin Cao, Yuan Cao, Jian Gao +1

Let $F_{p^{m}}$ be a finite field of cardinality $p^{m}$ and $R = F_{p^{m}} [u] / ⟨ u^{2} ⟩ = F_{p^{m}} + u F_{p^{m}}$ $(u^{2} = 0)$ , where $p$ is a prime and…

cs.IT2015★ 1 cited

Cyclic codes over $F_{2^{m}} [u] / ⟨ u^{k} ⟩$ of oddly even length

Yonglin Cao, Yuan Cao, Fang-Wei Fu

Let $F_{2^{m}}$ be a finite field of characteristic $2$ and $R = F_{2^{m}} [u] / ⟨ u^{k} ⟩ = F_{2^{m}} + u F_{2^{m}} + \dots + u^{k - 1} F_{2^{m}}$ ($u…

cs.IT2015

On $(α + u β)$ -constacyclic codes of length $p^{s} n$ over $F_{p^{m}} + u F_{p^{m}}$

Yuan Cao, Qingguo Li

Let $F_{p^{m}}$ be a finite field of cardinality $p^{m}$ and $R = F_{p^{m}} [u] / ⟨ u^{2} ⟩ = F_{p^{m}} + u F_{p^{m}}$ $(u^{2} = 0)$ , where $p$ is an odd prime…

cs.IT2015

On a class of $(δ + α u^{2})$ -constacyclic codes over $F_{q} [u] / ⟨ u^{4} ⟩$

Yuan Cao, Yonglin Cao, Jian Gao

Let $F_{q}$ be a finite field of cardinality $q$ , $R = F_{q} [u] / ⟨ u^{4} ⟩ = F_{q} + u F_{q} + u^{2} F_{q} + u^{3} F_{q}$ $(u^{4} = 0)$ whi…

Construction and enumeration of left dihedral codes satisfying certain duality properties

An explicit expression for Euclidean self-dual cyclic codes of length 2k over Galois ring GR(4,m)

On self-duality and hulls of cyclic codes over ⟨uk⟩F2m​[u]​ with oddly even length

Construction and enumeration for self-dual cyclic codes of even length over F2m​+uF2m​

An efficient method to construct self-dual cyclic codes of length ps over Fpm​+uFpm​

Explicit representation for a class of Type 2 constacyclic codes over the ring F2m​[u]/⟨u2λ⟩ with even length

Self-dual binary [8m,4m]-codes constructed by left ideals of the dihedral group algebra F2​[D8m​]

An explicit representation and enumeration for self-dual cyclic codes over F2m​+uF2m​ of length 2s

An explicit representation and enumeration for negacyclic codes of length 2kn over Z4​+uZ4​

A class of repeated-root constacyclic codes over Fpm​[u]/⟨ue⟩ of Type 2

Matrix-product structure of constacyclic codes over finite chain rings Fpm​[u]/⟨ue⟩

Negacyclic codes over the local ring Z4​[v]/⟨v2+2v⟩ of oddly even length and their Gray images

Complete classification for simple root cyclic codes over local rings Zps​[v]/⟨v2−pv⟩

Matrix-product structure of repeated-root constacyclic codes over finite fields

On a class of constacyclic codes over the non-principal ideal ring Zps​+uZps​

The Gray image of constacyclic codes over the finite chain ring Fpm​[u]/⟨uk⟩

Complete classification of (δ+αu2)-constacyclic codes over F2m​[u]/⟨u4⟩ of oddly even length

Left dihedral codes over Galois rings GR(p2,m)

Constacyclic codes of length psn over Fpm​+uFpm​

Cyclic codes over F2m​[u]/⟨uk⟩ of oddly even length

On (α+uβ)-constacyclic codes of length psn over Fpm​+uFpm​

On a class of (δ+αu2)-constacyclic codes over Fq​[u]/⟨u4⟩

An explicit expression for Euclidean self-dual cyclic codes of length $2^{k}$ over Galois ring $GR (4, m)$

On self-duality and hulls of cyclic codes over $\frac{F _{2^{m}} [ u ]}{⟨ u ^{k} ⟩}$ with oddly even length

Construction and enumeration for self-dual cyclic codes of even length over $F_{2^{m}} + u F_{2^{m}}$

An efficient method to construct self-dual cyclic codes of length $p^{s}$ over $F_{p^{m}} + u F_{p^{m}}$

Explicit representation for a class of Type 2 constacyclic codes over the ring $F_{2^{m}} [u] / ⟨ u^{2 λ} ⟩$ with even length

Self-dual binary $[8 m, 4 m]$ -codes constructed by left ideals of the dihedral group algebra $F_{2} [D_{8 m}]$

An explicit representation and enumeration for self-dual cyclic codes over $F_{2^{m}} + u F_{2^{m}}$ of length $2^{s}$

An explicit representation and enumeration for negacyclic codes of length $2^{k} n$ over $Z_{4} + u Z_{4}$

A class of repeated-root constacyclic codes over $F_{p^{m}} [u] / ⟨ u^{e} ⟩$ of Type $2$

Matrix-product structure of constacyclic codes over finite chain rings $F_{p^{m}} [u] / ⟨ u^{e} ⟩$

Negacyclic codes over the local ring $Z_{4} [v] / ⟨ v^{2} + 2 v ⟩$ of oddly even length and their Gray images

Complete classification for simple root cyclic codes over local rings $Z_{p^{s}} [v] / ⟨ v^{2} - p v ⟩$

On a class of constacyclic codes over the non-principal ideal ring $Z_{p^{s}} + u Z_{p^{s}}$

The Gray image of constacyclic codes over the finite chain ring $F_{p^{m}} [u] / ⟨ u^{k} ⟩$

Complete classification of $(δ + α u^{2})$ -constacyclic codes over $F_{2^{m}} [u] / ⟨ u^{4} ⟩$ of oddly even length

Left dihedral codes over Galois rings $GR (p^{2}, m)$

Constacyclic codes of length $p^{s} n$ over $F_{p^{m}} + u F_{p^{m}}$

Cyclic codes over $F_{2^{m}} [u] / ⟨ u^{k} ⟩$ of oddly even length

On $(α + u β)$ -constacyclic codes of length $p^{s} n$ over $F_{p^{m}} + u F_{p^{m}}$

On a class of $(δ + α u^{2})$ -constacyclic codes over $F_{q} [u] / ⟨ u^{4} ⟩$