New self-dual codes from TGRS codes with general $ \ell $ twists

Yun Ding; Shixin Zhu

doi:10.3934/amc.2024017

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2025, Volume 19, Issue 2: 662-675. Doi: 10.3934/amc.2024017

This issue Previous Article New spectrally null constrained mutually orthogonal complementary sets and Z-complementary code sets Next Article Linear codes invariant under a linear endomorphism

New self-dual codes from TGRS codes with general $ \ell $ twists

Yun Ding and
Shixin Zhu^,

School of Mathematics, Hefei University of Technology, Hefei, China

^*Corresponding author: Shixin Zhu
^*Corresponding author: Shixin Zhu

Received: January 2024

Early access: May 11, 2024

Published online: May 11, 2024

This research is supported by National Natural Science Foundation of China under Grant Nos. 12171134 and U21A20428.

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Abstract

Twisted generalized Reed-Solomon (TGRS) codes are generalizations of generalized Reed-Solomon (GRS) codes. It is widely recognized that GRS codes are maximum distance sparable (MDS) codes, but TGRS codes are not necessarily MDS. In this paper, we give a condition that is both sufficient and necessary for twisted generalized Reed-Solomon codes with general $ \ell $ twists ($ \ell $-TGRS codes) to be MDS. For $ \ell $-TGRS codes to be self-dual, we also propose a condition that is both sufficient and necessary. Furthermore, we consider three special cases of $ \ell $ twists and present two new and explicit constructions of self-dual $ \ell $-TGRS codes.

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Mathematics Subject Classification: 94B05.

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