On the duals of geometric Goppa codes from norm-trace curves

Edoardo Ballico, Alberto Ravagnani

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

3 Citaten (Scopus)

Samenvatting

In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric approach is performed and applied to study in particular the dual codes of one-point and two-point codes arising from norm-trace curves through Goppas construction, providing in many cases their minimum distance and some bounds on the number of their minimum-weight codewords. The results are obtained by showing that the supports of the minimum-weight codewords of the studied codes obey some precise geometric laws as zero-dimensional subschemes of the projective plane. Finally, the dimension of some classical two-point Goppa codes on norm-trace curves is explicitely computed.

Originele taal-2Engels
Pagina's (van-tot)30-39
Aantal pagina's10
TijdschriftFinite Fields and their Applications
Volume20
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - mrt. 2013
Extern gepubliceerdJa

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