New Codes for the Berlekamp-Massey-Sakata Algorithm

Finite Fields and their Applications

Volumn 7, Issue 2, 2001, Pages 293-317

  O'Sullivan, Michael E ^a  

^a UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

Algebraic geometry codes; Berlekamp Massey algorithm; order function; valution ring

Indexed keywords

EID: 0005742820     PISSN: 10715797     EISSN: None     Source Type: Journal    
DOI: 10.1006/ffta.2000.0283     Document Type: Article

References (15)

1. Atiyah M. F., MacDonald I. G. Introduction to Commutative Algebra. 1969;Addison-Wesley, Reading.
2. Beckmann P., Stückrad J. The concept of Gröbner algebras. J. Symbolic Comput. 10:1990;465-479.
3. Bourbaki N. Commutative Algebra. 1972;Addison-Wesley, Reading.
4. Cox D., Little J., O'Shea D. Ideals, Varieties, and Algorithms. 1997;Springer-Verlag, Berlin/New York.
5. Hartshorne R. Algebraic Geometry. 1977;Springer-Verlag, Berlin/New York.
6. Høholdt T., Pellikaan R., van Lint J. H. Algebraic geometry codes. Huffmann W. C., Pless V. Handbook of Coding Theory. 1998;871-961 Elsevier, Amsterdam/New York.
7. O'Sullivan M. E. Decoding of codes defined by a single point on a curve. IEEE Trans. Inform. Theory. 41:1995;1709-1719.
8. M. E. O'Sullivan, The key equation for one-point codes and efficient error evaluation, submitted for publication.
9. Pellikaan R., Kirfel C. The minimum distance of codes in an array coming from telescopic semigroups. IEEE Trans. Inform. Theory. 41:1995;1720-1732.
10. Robbiano L. On the theory of graded structures. J. Symbolic Comput. 2:1986;139-170.
11. Sakata S. Extension of the Berlekamp-Massey algorithm to N dimensions. Inform. and Comput. 84:1990;207-239.
12. Seidenberg A. Elements of the Theory of Algebraic Curves. 1968;Addison-Wesley, Reading.
13. Spivakovsky M. Valuations in function fields of surfaces, Amer. J. Math. 112:1990;107-156.
14. M. Sweedler, Ideal bases and valuation rings, preprint.
15. Zariski O. The reduction of singularities of an algebraic surface. Ann. of Math. 40:1939;639-689.