Counting Extended Irreducible Goppa Codes
نویسندگان
چکیده
We obtain an upper bound on the number of extended irreducible q-ary Goppa codes of degree r and length q + 1, where q = p and n and r > 2 are prime numbers.
منابع مشابه
Interesting Examples on Maximal Irreducible Goppa Codes
In this paper a full categorization of irreducible classical Goppa codes of degree 4 and length 9 is given. It is an interesting example in the context of find the number of permutation non-equivalent classical irreducible maximal Goppa codes having fixed parameters q, n and r using group theory techniques.
متن کاملList Decoding for Binary Goppa Codes
This paper presents a list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n− p n(n− 2t− 2) errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomialtime list-decoding algorithms for the same codes, the new algorithm corrects approximately t/2n extra errors.
متن کاملEnumeration of inequivalent irreducible Goppa codes
We consider irreducible Goppa codes over Fq of length q n defined by polynomials of degree r where q is a prime power and n, r are arbitrary positive integers. We obtain an upper bound on the number of such codes.
متن کاملPermutation equivalent maximal irreducible Goppa codes
We consider the problem of finding the number of permutation nonequivalent classical irreducible maximal Goppa codes having fixed parameters q, n and r from a group theory point of view.
متن کاملGenerating Goppa Codes
Once quantum computers become operational all current public key crypto systems, PKCSs become obsolete. Fortunately, there are alternative quantum computer robust methods based on coding, on hashing, on multivariate polynomials, on lattices etc. One such candidate is the McEliece PKCS which is based on error correcting codes, e.g. Goppa codes. Hence, in order to implement the McEliece PKCS one ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2018