Abstract
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.
Original language | English |
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Pages (from-to) | 30-39 |
Number of pages | 10 |
Journal | Finite Fields and their Applications |
Volume | 20 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2013 |
Externally published | Yes |
Keywords
- Minimum distance
- Minimum-weight codeword
- Norm-trace curve