Enumeration of Extended Irreducible Binary Goppa Codes of Degree 7 and length 65.
Abstract
In this paper we count extended irreducible binary Goppa codes of length
65 and degree 7. We do this by considering the tools used to count non extended version.
Full Text:
PDFReferences
Loidreau, P., and Sendrier, N., "Weak keys in the McEliece public key cryptosystem," IEEE Transactions on Information Theory, pp. 1207-1211, available at http://perso.univrennes1.fr/pierre.loidreau/articles/ieee-it/ClesFaibles.pdf, (2001).
____________________________________________________________
Overbeck, R.: "Structural attacks for public key cryptosystems based on
Gabidulin codes." Journal of Cryptology 21(2), 280–301 (2008).
____________________________________________________________
Wieschebrink, C.: "Cryptanalysis of the Niederreiter public key scheme
based on GRS subcodes". In: Sendrier, N. (ed.) Post-Quantum Cryptography (PQCrypto 2010), Lecture Notes in Computer Science 6061, 61–72. Springer (2010).
____________________________________________________________
Baldi, M., "Enhanced public key security for the McEliece cryptosystem," J Cryptol (2016) 29:doi:10.1007/s00145-014-9187-8
____________________________________________________________
Lidl, R., and Niederreiter, H., "Finite Fields." Cambridge University Press, 1983.
____________________________________________________________
Magamba K., and Ryan J.A., "Counting Irreducible Polynomials of degree r over $F_{q^n}$ and Generating Goppa Codes using the Lattice of Subfields of $F_{q^{nr}}$," Journal of Discrete Mathematics, (2014).
____________________________________________________________
J.A. Ryan, 2004, "Irreducible Goppa Codes", PhD Thesis, University College Cork.
____________________________________________________________
C.L. Chen, "Equivalent irreducible Goppa codes," IEEE Trans. Inform. Theory,relax -24,766-769, 1978.
Ryan J.A., "Counting Extended Irreducible Goppa Codes", Discrete Mathematics, (2014).
Refbacks
- There are currently no refbacks.
MAYFEB Journal of Mathematics
Toronto, Ontario, Canada
MAYFEB TECHNOLOGY DEVELOPMENT
ISSN 2371-6193