CSpace
Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings
Lu, PH; Liu, ML; Oberst, U
2004
Source PublicationACTA APPLICANDAE MATHEMATICAE
ISSN0167-8019
Volume80Issue:2Pages:175-198
AbstractThis 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.
KeywordNullstellensatz quasi-Frobenius ring linear recurring array multidimensional linear system annihilating ideal duality cyclic code
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000188607500002
PublisherSPRINGER
Citation statistics
Cited Times:13[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/19379
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Lu, PH]'s Articles
[Liu, ML]'s Articles
[Oberst, U]'s Articles
Baidu academic
Similar articles in Baidu academic
[Lu, PH]'s Articles
[Liu, ML]'s Articles
[Oberst, U]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Lu, PH]'s Articles
[Liu, ML]'s Articles
[Oberst, U]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.