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Enumeration of Extended Irreducible Binary Goppa Codes.
- Source :
- IEEE Transactions on Information Theory; Aug2022, Vol. 68 Issue 8, p5145-5153, 9p
- Publication Year :
- 2022
-
Abstract
- The family of Goppa codes is one of the most interesting subclasses of linear codes. As the McEliece cryptosystem often chooses a random Goppa code as its key, knowledge of the number of inequivalent Goppa codes for fixed parameters may facilitate in the evaluation of the security of such a cryptosystem. In this paper we present a new approach to give an upper bound on the number of inequivalent extended irreducible binary Goppa codes. To be more specific, let $n>3$ be an odd prime number and $q=2^{n}$ ; let $r\geq 3$ be a positive integer satisfying $\gcd (r,n)=1$ and $\gcd \big (r,q(q^{2}-1)\big)=1$. We obtain an upper bound for the number of inequivalent extended irreducible binary Goppa codes of length $q+1$ and degree $r$. [ABSTRACT FROM AUTHOR]
- Subjects :
- BINARY codes
LINEAR codes
PRIME numbers
ODD numbers
CRYPTOSYSTEMS
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 157958031
- Full Text :
- https://doi.org/10.1109/TIT.2022.3166847