OPTIMAL BINARY CODES FROM ONE-LEE WEIGHT CODES AND TWO-LEE WEIGHT PROJECTIVE CODES OVER Z_4
查看参考文献19篇
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文摘
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This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z_4. The authors first give the Pless identities on the Lee weight of linear codes over Z_4. Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively, the construction methods of one-Lee weight and two-Lee weight projective codes over Z_4 are also given. Finally, the authors recall the weight-preserving Gray map from (Z_4~n, Lee weight) to (F_2~(2n), Hamming weight), and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes, which reach the Plotkin bound and the Griesmer bound. |
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来源
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Journal of Systems Science and Complexity
,2014,27(4):795-810 【核心库】
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DOI
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10.1007/s11424-014-2188-8
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关键词
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Gray map
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Lee weight
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one-weight codes
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projective codes
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two-weight codes
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地址
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1.
School of Mathematical Sciences, Anhui University, Hefei, 230601
2.
Department of Mathematics and Physics, Hefei University, Hefei, 230601
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语种
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英文 |
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文献类型
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研究性论文 |
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ISSN
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1009-6124 |
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学科
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数学 |
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基金
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国家自然科学基金
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Talents youth Fund of Anhui Province Universities
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The second author of this paper is supported by Key Discipline Construction of Hefei University
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文献收藏号
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CSCD:5314368
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参考文献 共
19
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