Counting irreducible Goppa codes
نویسندگان
چکیده
منابع مشابه
Counting Extended Irreducible Goppa Codes
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.
متن کاملInteresting 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 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 کاملGoppa codes
Absfruct-Goppa described a new class of linear noncyclic errorcorrecting codes in [l] and [2]. This paper is a summary of Goppa’s work, which is not yet available in English.’ We prove the four most important properties of Goppa codes. 1) There exist q-ary Goppa codes with lengths and redundancies comparable to BCH codes. For the same redundancy, the Goppa code is typically one digit longer. 2)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2001
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700002949