@article{Zheng2023, 
author = {Xiying Zheng and Bo Kong and Yao Yu},
title = {Quantum codes from    σ-dual-containing constacyclic codes over              R              l      ,      k},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24075-24086},
keywords = {quantum codes, σ-self-orthogonal, σ-dual-containing, constacyclic codes, CSS construction, Hermitian construction},
url = {https://www.sciopen.com/article/10.3934/math.20231227},
doi = {10.3934/math.20231227},
abstract = {Let              R              l      ,      k        =                    F                            p        m              [      u    1    ,      u    2    ,  ⋯  ,      u    k    ]      /    ⟨      u          i              l        =      u          i        ,      u    i        u    j    =      u    j        u    i    =  0  ⟩, where    p is a prime,    l is a positive integer,    (  l  −  1  )  ∣  (  p  −  1  ) and    1  ≤  i  ,  j  ≤  k. First, we define a Gray map        ϕ          l      ,      k       from              R              l      ,      k        n   to                      F                            p        m                    (      (      l      −      1      )      k      +      1      )      n      , and study its Gray image. Further, we study the algebraic structure of    σ-self-orthogonal and    σ-dual-containing constacyclic codes over              R              l      ,      k      , and give the necessary and sufficient conditions for    λ-constacyclic codes over              R              l      ,      k       to satisfy    σ-self-orthogonal and    σ-dual-containing. Finally, we construct quantum codes from    σ-dual-containing constacyclic codes over              R              l      ,      k       using the CSS construction or Hermitian construction and compare new codes our obtained better than the existing codes in some recent references.}
}