Galois self-orthogonal constacyclic codes over finite fields

Fu, Yuqing; Liu, Hongwei

doi:10.1007/s10623-021-00957-6

Cited by 8 publications

(1 citation statement)

References 25 publications

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“…As far as we know, there is not much researches and constructions on Galois selforthogonal codes. In [50] (2) According to [19], arbitrary dimension Galois hull linear codes can also be used to construct EAQECCs, so using Theorems 10 and 11, we can get many new EAQECCs based on e-Galois selforthogonal codes. And for the consistency of the text, we give the specific theorems in Section 5.…”

Section: Remark 3 (1)mentioning

confidence: 99%

On Arbitrary Dimension Hermitian Hull linear codes from Hermitian self-orthogonal codes and New Hermitian Self-Orthogonal GRS Codes

Li¹,

Zhu²

2022

Preprint

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Due to the important role of hulls of linear codes in coding theory, the problem about constructing arbitrary dimension hull linear codes has become a hot issue. In this paper, we generalize conclusions in [41] and [42] and prove that the self-orthogonal codes of length n can construct linear codes of length n + 2i and n + 2i + 1 with arbitrary-dimensional hulls under the special Hermitian inner product and the general e-Galois inner product for any integers i ≥ 0. Then four new classes of Hermitian self-orthogonal GRS or extend GRS codes are constructed via two known multiplicative coset decompositions of F q 2 . The codes we constructed can be used to obtain new arbitrary dimension Galois hull linear codes by Theorems 11 and 12 in [21] and finally we get many new EAQECCs whose code lengths can take n + 2i and n + 2i + 1.

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Section: Remark 3 (1)mentioning

confidence: 99%