New MDS Euclidean Self-Orthogonal Codes

Fang, Xiaolei; Liu, Meiqing; Luo, Jinquan

doi:10.1109/tit.2020.3020986

Cited by 25 publications

(14 citation statements)

References 20 publications

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“…The following two lemmas (or with some equivalent forms) ensure the existence of MDS self-dual codes. The reader may refer to [17,22,6,23,8,18,11,9,10] for more details.…”

Section: Preliminariesmentioning

confidence: 99%

“…The extreme case is Euclidean almost self-dual code, i.e., C is called a Euclidean almost self-dual code if C ⊆ C ⊥ and dim(C ⊥ ) = dim(C) + 1. There are few works on construction of Euclidean almost self-dual codes and the reader may refer to [9].…”

Section: Introductionmentioning

confidence: 99%

“…Naturally, as a more special class of codes, MDS self-dual codes have potential applications in coding theory, cryptography and combinatorics [13,14,15]. Moreover, MDS self-orthogonal codes have been employed to construct quantum MDS codes [20,7] and the reader may refer to [9,24,19,5] for the constructions of self-orthogonal codes.…”

Section: Introductionmentioning

confidence: 99%

“…In [11], the authors considered the evaluation sets as a subgroup of finite fields and its cosets in a bigger subgroup. Fang et al [9] took the union of two disjoint multiplicative subgroups and their cosets as the evaluation sets. In [10], the authors considered the evaluation sets as two multiplicative subgroups and their cosets which have nonempty intersection.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, inspired by the idea of [9], we give four new families of MDS selfdual codes with flexible parameters by generalizing the evaluation sets in [9] to the generic forms. The lengths of codes produced by our constructions can be expressed as a linear combination of two divisors of q −1.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Generic constructions of MDS Euclidean self-dual codes via GRS codes

Huang¹,

Fang²,

Fu³

et al. 2023

AMC

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<p style='text-indent:20px;'>Recently, the construction of new MDS Euclidean self-dual codes has been widely investigated. In this paper, for square <inline-formula><tex-math id="M1">\begin{document}$ q $\end{document}</tex-math></inline-formula>, we utilize generalized Reed-Solomon (GRS) codes and their extended codes to provide four generic families of <inline-formula><tex-math id="M2">\begin{document}$ q $\end{document}</tex-math></inline-formula>-ary MDS Euclidean self-dual codes of lengths in the form <inline-formula><tex-math id="M3">\begin{document}$ s\frac{q-1}{a}+t\frac{q-1}{b} $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M4">\begin{document}$ s $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ t $\end{document}</tex-math></inline-formula> range in some interval and <inline-formula><tex-math id="M6">\begin{document}$ a, b \,|\, (q -1) $\end{document}</tex-math></inline-formula>. In particular, for large square <inline-formula><tex-math id="M7">\begin{document}$ q $\end{document}</tex-math></inline-formula>, our constructions take up a proportion of generally more than 34% in all the possible lengths of <inline-formula><tex-math id="M8">\begin{document}$ q $\end{document}</tex-math></inline-formula>-ary MDS Euclidean self-dual codes, which is larger than the previous results. Moreover, two new families of MDS Euclidean self-orthogonal codes and two new families of MDS Euclidean almost self-dual codes are given similarly.</p>

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“…The following two lemmas (or with some equivalent forms) ensure the existence of MDS self-dual codes. The reader may refer to [17,22,6,23,8,18,11,9,10] for more details.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%