Four classes of LCD codes from (*)-(L,P)-twisted generalized Reed-Solomon codes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915501311000576 |
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| author | Liang, Zhonghao Liao, Qunying |
| author_facet | Liang, Zhonghao Liao, Qunying |
| contents | It's well-known that maximum distance separable codes (in short, MDS) and linear complementary dual (in short, LCD) codes are very important in coding theory and practice. In 2023, Yue et al. [25] constructed three classes of LCD MDS codes via (*)-TGRS codes. Recently, Wu et al. [27] generalized the results given by Yue et al. and constructed several classes of LCD MDS codes. In this paper, we unify their constructions by defining the (*)-(L,P)-twisted generalized Reed-Solomon (in short, (*)-(L,P)-TGRS) code, give the parity-check matrix of (*)-(L,P)-TGRS codes, and then construct four classes of LCD codes. Finally, some corresponding examples are given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Four classes of LCD codes from (*)-(L,P)-twisted generalized Reed-Solomon codes Liang, Zhonghao Liao, Qunying Information Theory 11T06 E.4 It's well-known that maximum distance separable codes (in short, MDS) and linear complementary dual (in short, LCD) codes are very important in coding theory and practice. In 2023, Yue et al. [25] constructed three classes of LCD MDS codes via (*)-TGRS codes. Recently, Wu et al. [27] generalized the results given by Yue et al. and constructed several classes of LCD MDS codes. In this paper, we unify their constructions by defining the (*)-(L,P)-twisted generalized Reed-Solomon (in short, (*)-(L,P)-TGRS) code, give the parity-check matrix of (*)-(L,P)-TGRS codes, and then construct four classes of LCD codes. Finally, some corresponding examples are given. |
| title | Four classes of LCD codes from (*)-(L,P)-twisted generalized Reed-Solomon codes |
| topic | Information Theory 11T06 E.4 |
| url | https://arxiv.org/abs/2509.14878 |