@article{Zhou2026, 
author = {Juncheng Zhou and Hongfeng Wu},
title = {Cyclotomy, cyclotomic cosets and arithmetic properties of some families in                                F                l            [      x      ]              ⟨              x                              p            s                                q            t                              −      1      ⟩},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {10049-10078},
keywords = {cyclotomy, cyclotomic cosets, cyclotomic numbers, cyclic codes, finite fields},
url = {https://www.sciopen.com/article/10.3934/math.2026415},
doi = {10.3934/math.2026415},
abstract = {Arithmetic properties of some families in              F        l    [  x  ]      /    ⟨      x                  p        s                    q        t              −  1  ⟩ were obtained by using the cyclotomic classes of order 2 with respect to    n  =      p    s        q    t  , where    p  ≡  3        m    o    d      4,    gcd  (  ϕ  (      p    s    )  ,  ϕ  (      q    t    )  )  =  2,    l is a primitive root modulo        q    t  , and              o      r      d                      p        s              (  l  )  =  ϕ  (      p    s    )      /    2. The form of these cyclotomic classes enabled us to further generalize the results obtained in [1]. The explicit expressions of primitive idempotents of minimal ideals in              F        l    [  x  ]      /    ⟨      x                  p        s                    q        t              −  1  ⟩ were also obtained.}
}