| 张爱仙,张思敏.环F2+uF2+u2F2上低Lee重码的构造[J].数学年刊A辑,2024,45(3):309~318 |
| 环F2+uF2+u2F2上低Lee重码的构造 |
| Constructions of Few-Lee Weight Codes over F2+uF2+u2F2 |
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| DOI：10.16205/j.cnki.cama.2024.0022 |
| 中文关键词: 低重码 Gray映射 单纯复形 重量分布 |
| 英文关键词:Few-Weight codes Gray mapping Simplicial complex Weight distribution |
| 基金项目:国家自然科学基金(No.12101492)； 陕西省自然科学基金(No.2022JM-017)； 西安市科技计划(No.23GXFW0065) |
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| 中文摘要: |
| 低重码在秘密共享方案以及认证码等领域有重要的应用.本文选取的环为R=F2+uF2+u2F2,u3=0.首先通过F2m上的单纯复形构造了环R上的十类线性码,接着利用特征函数和Gray映射计算了这些码的Lee重量分布.发现它们都是低Lee重的. |
| 英文摘要: |
| Codes with few-weight have important applications in the fields of secret sharing schemes and authentication codes.In this paper,the authors choose F2+uF2+u2F2,u3=0 as the ring.First,the authors construct ten classes of linear codes over ring R by simplicial complexes over Fm2.Then the authors calculate the Lee weight distribution of these codes by using eigenfunction and Gray mapping. |
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