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On Cyclic Codes in Incidence Rings


Alfaro, R and Kelarev, AV, On Cyclic Codes in Incidence Rings, Studia Scientiarum Mathematicarum Hungarica, 43, (1) pp. 69-77. ISSN 0081-6906 (2006) [Refereed Article]

DOI: doi:10.1556/SScMath.43.2006.1.5


Cyclic codes are defined as ideals in polynomial quotient rings. We are using a matrix ring construction in a similar way to define classes of codes. It is shown that all cyclic and all linear codes can be embedded as ideals in this construction. A formula for the largest Hamming weight of one-sided ideals in incidence rings is given. It is shown that every incidence ring defined by a directed graph always possesses a principal one-sided ideal that achieves the optimum Hamming weight. © 2006 Akadémiai Kiadó, Budapest.

Item Details

Item Type:Refereed Article
Research Division:Information and Computing Sciences
Research Group:Data management and data science
Research Field:Information retrieval and web search
Objective Division:Manufacturing
Objective Group:Computer, electronic and communication equipment
Objective Field:Voice and data equipment
UTAS Author:Kelarev, AV (Dr Andrei Kelarev)
ID Code:39567
Year Published:2006
Funding Support:Australian Research Council (DP0449469)
Web of Science® Times Cited:8
Deposited By:Computing
Deposited On:2006-08-01
Last Modified:2007-04-24

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