Algebraic methods for the distance of cyclic codes

Piva, Matteo (2014) Algebraic methods for the distance of cyclic codes. PhD thesis, University of Trento.

PDF - Doctoral Thesis


In this thesis we provide known and new results which explain the relationship between the actual minimum distance of cyclic codes, bounds that use only information on the defining sets of cyclic codes to lower bound the distance (root bounds) and bounds that also need the knowledge of the defining sets of all cyclic subcodes (border bounds). We propose a new bound which is provably better of many known bounds and that can be computed in polynomial time with respect to the length of the code. We sketch how to use the generalized Newton identities to give alternative proofs of known bounds. Finally, we use Groebner bases to prove that the optimal root bound can be computed in finite time.

Item Type:Doctoral Thesis (PhD)
Doctoral School:Mathematics
PhD Cycle:XXVI
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/02 ALGEBRA
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