| 环Fp+vFp上线性码的极小支座谱 |
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| 引用本文： | 张光辉. 环Fp+vFp上线性码的极小支座谱[J]. 电子学报, 2015, 43(8): 1621-1626. DOI: 10.3969/j.issn.0372-2112.2015.08.023 |
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| 作者姓名： | 张光辉 |
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| 作者单位： | 洛阳师范学院数学科学学院, 河南洛阳 471022 |
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| 摘 要： | 基于环Fp+vFp(v2=v)上线性码的一种直和分解,利用环Fp+vFp上的线性码的Torsion码,把环Fp+vFp上的线性码的极小支座谱的确定归结于有限域上的情形;进一步探讨了环Fp+vFp上的线性码的校验矩阵,利用该校验矩阵确定了环Fp+vFp上的线性码的对偶码的极小支座谱;最后利用环上的线性码的极小支座谱,探讨了环Fp+vFp上线性码的最小Hamming距离,并且给出了一个环Fp+vFp上最小Hamming距离为d的线性码的构造方法,这里p是任一个素数,d是一个正整数.
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| 关 键 词： | 环Fp+vFp 支座 极小支座谱 Hamming距离 |
| 收稿时间： | 2013-11-07 |
On the Minimum Support Hierarchy of Linear Codes over Fp +vFp |
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| ZHANG Guang-hui. On the Minimum Support Hierarchy of Linear Codes over Fp +vFp[J]. Acta Electronica Sinica, 2015, 43(8): 1621-1626. DOI: 10.3969/j.issn.0372-2112.2015.08.023 |
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| Authors: | ZHANG Guang-hui |
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| Affiliation: | School of Mathematical Sciences, Luoyang Normal University, Luoyang, Henan, 471022, China |
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| Abstract: | Based on the direct sum decomposition of linear codes over Fp+vFp(v2=v), the minimum support hierarchy of linear codes over Fp+vFp and their dual codes are studied by means of the Torsion codes and parity check matrice of these linear codes.With these results the Hamming distance of linear codes over Fp+vFp are determined in terms of that of linear codes over the finite field Fpand an explicit construction for linear codes over Fp+vFp are given with the Hamming distance d, wherepis a prime and dis a positive integer. |
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| Keywords: | Fp+vFp support minimum support hierarchy Hamming distance |
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