Gröbner Bases over Commutative Rings and Applications to Coding Theory

Eimear Byrne () and Teo Mora ()
Additional contact information
Eimear Byrne: University College, School of Mathematical Sciences
Teo Mora: University of Genoa, Department of Information Theory

A chapter in Gröbner Bases, Coding, and Cryptography, 2009, pp 239-261 from Springer

Abstract: Abstract We give a survey of results and applications relating to the theory of Gröbner bases of ideals and modules where the coefficient ring is a finite commutative ring. For applications, we specialize to the case of a finite chain ring. We discuss and compare the main algorithms that may be implemented to compute Gröbner and (in the case of a chain ring) Szekeres-like bases. We give an account of a number of decoding algorithms for alternant codes over commutative finite chain rings.

Keywords: Commutative rings; Finite chain rings; Galois ring; Gröbner bases; Szekeres-like bases; Buchberger’s algorithm; Key-equation; Solution module; Berlekamp–Massey algorithm; FGLM algorithm; Alternant codes; Decoding algorithms; List decoding (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-93806-4_14

Ordering information: This item can be ordered from
http://www.springer.com/9783540938064

DOI: 10.1007/978-3-540-93806-4_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().