Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings
文献类型：期刊论文
| 作者 | Lu, PH; Liu, ML; Oberst, U |
| 刊名 | ACTA APPLICANDAE MATHEMATICAE
 |
| 出版日期 | 2004 |
| 卷号 | 80期号:2页码:175-198 |
| 关键词 | Nullstellensatz quasi-Frobenius ring linear recurring array multidimensional linear system annihilating ideal duality cyclic code |
| ISSN号 | 0167-8019 |
| 英文摘要 | This paper generalizes the duality between polynomial modules and their inverse systems (Macaulay), behaviors (Willems) or zero sets of arrays or multi-sequences from the known case of base fields to that of commutative quasi-Frobenius (QF) base rings or even to QF-modules over arbitrary commutative Artinian rings. The latter generalization was inspired by the work of Nechaev et al. who studied linear recurring arrays over QF-rings and modules. Such a duality can be and has been suggestively interpreted as a Nullstellensatz for polynomial ideals or modules. We also give an algorithmic characterization of principal systems. We use these results to define and characterize n-dimensional cyclic codes and their dual codes over QF rings for n > 1. If the base ring is an Artinian principal ideal ring and hence QF, we give a sufficient condition on the codeword lengths so that each such code is generated by just one codeword. Our result is the n-dimensional extension of the results by Calderbank and Sloane, Kanwar and Lopez-Permouth, Z. X. Wan, and Norton and Salagean for n = 1. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000188607500002 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/19378]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Lu, PH |
| 作者单位 | 1.Fudan Univ, Dept Comp Sci, Shanghai 200433, Peoples R China 2.Fudan Univ, Inst Math, Shanghai 200433, Peoples R China 3.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 4.Univ Innsbruck, Inst Math, A-6020 Innsbruck, Austria |
| 推荐引用方式 GB/T 7714 | Lu, PH,Liu, ML,Oberst, U. Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings[J]. ACTA APPLICANDAE MATHEMATICAE,2004,80(2):175-198. |
| APA | Lu, PH,Liu, ML,&Oberst, U.(2004).Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings.ACTA APPLICANDAE MATHEMATICAE,80(2),175-198. |
| MLA | Lu, PH,et al."Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings".ACTA APPLICANDAE MATHEMATICAE 80.2(2004):175-198. |
入库方式： OAI收割
来源：数学与系统科学研究院
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