TY  - JOUR
AU  - Song, Hao
AU  - Ren, Yuezhen
AU  - Li, Ruihu
AU  - Liu, Yang
PY  - 2025
TI  - Optimal quaternary Hermitian self-orthogonal    [  n  ,  5  ] codes of    n  ≥  492
JO  - AIMS Mathematics
SP  - 9324
EP  - 9331
VL  - 10
IS  - 4
AB  - Self-orthogonal (SO) codes, including Hermitian self-orthogonal (HSO) codes, form an important class of linear codes, and such codes have close connections to other mathematical structures such as block designs, lattices, and sphere packings, which can also be used to construct quantum codes. Many scholars try to solve the problem of determining low-dimensional optimal HSO codes over small fields as it is done for optimal linear codes. Let        d          o        (  n  ,  k  ) be the minimum distance of an optimal quaternary    [  n  ,  k  ] linear code, and        d          s      o        (  n  ,  k  ) be that of an optimal quaternary    [  n  ,  k  ] HSO code. In this paper, we try to determine        d          s      o        (  n  ,  5  ) for    n  ≥  492 by constructing quaternary    [  n  ,  5  ] HSO codes in detail. Some disjoint HSO blocks have been found from generator matrices of some special optimal HSO codes. These special optimal HSO codes are constructed from quaternary simplex codes and McDonald codes. Then,    [  n  ,  5  ] HSO codes have been constructed for    n  ≥  492, by removing those special blocks from the known optimal HSO codes. As a result, we could show    [  n  ,  5  ,      d          s      o        (  n  ,  5  )  ]    =  [  n  ,  5  ,  2  ⌊                    d                  o                    (      n      ,      5      )        2    ⌋  ] for    n  ≥  492.
UR  - https://doi.org/10.3934/math.2025430
DO  - 10.3934/math.2025430