Griesmer bound and constructions of linear codes in b-symbol metric
The b-symbol metric is a generalization of the Hamming metric. Linear codes in the b-symbol metric have been used in the read channel whose outputs consist of b consecutive symbols. The Griesmer bound outperforms the Singleton bound for Fq-linear codes in the Hamming metric, when q is fixed and the...
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| المؤلفون الرئيسيون: | , , , , |
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| مؤلفون آخرون: | |
| التنسيق: | مقال |
| اللغة: | English |
| منشور في: |
2024
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/10356/181878 |
| الوسوم: |
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| المؤسسة: | Nanyang Technological University |
| اللغة: | English |
| الملخص: | The b-symbol metric is a generalization of the Hamming metric. Linear codes in the b-symbol metric have been used in the read channel whose outputs consist of b consecutive symbols. The Griesmer bound outperforms the Singleton bound for Fq-linear codes in the Hamming metric, when q is fixed and the length is large enough. This scenario is also applicable in the b-symbol metric. Shi, Zhu, and Helleseth recently made a conjecture on cyclic codes in the b-symbol metric. In this paper, we present the b-symbol Griesmer bound for linear codes by concatenating linear codes and simplex codes. Based on cyclic codes and extended cyclic codes, we propose two families of distance-optimal linear codes with respect to the b-symbol Griesmer bound. |
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