Convolutional Goppa codes
نویسندگان
چکیده
منابع مشابه
One dimensional Convolutional Goppa Codes over the projective line
We give a general method to construct MDS one-dimensional convolutional codes. Our method generalizes previous constructions [5]. Moreover we give a classification of one-dimensional Convolutional Goppa Codes and propose a characterization of MDS codes of this type. Introduction One of the main problems in coding theory is the construction of codes with a large distance, such as so-called MDS c...
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 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 کاملNotes on Goppa Codes
Ideas from algebraic geometry became useful in coding theory after Goppa’s construction [7]. He had the beautiful idea of associating to a (projective, geometrically irreducible, non-singular, algebraic) curve X defined over Fq, the finite field with q elements, a code C. This code is constructed from two divisors D and G on X , where one of them, say D, is the sum of n distinct Fq-rational poi...
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We investigate a relation between generalized algebraic geometry codes and geometric Goppa codes. We also propose a decoding method for algebraic geometry codes.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2006
ISSN: 0018-9448
DOI: 10.1109/tit.2005.860447