Construction and decoding of a class of algebraic geometry codes
نویسندگان
چکیده
Absfruct We construct a class of codes derived from algebraic plane curves. The concepts and results from algebraic geometry we use are explained in detail, and no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH codes.
منابع مشابه
On construction and generalization of algebraic geometry codes
The construction, estimation of minimum distance, and decoding algorithms of algebraic geometry codes can be explained without using advanced mathematics by the notion of weight domains. We clarify the relation between algebraic geometry codes and linear codes from weight domains. Then we review a systematic construction which yields all weight domains.
متن کاملA class of Sudan-decodable codes
In this correspondence, Sudan’s algorithm is modified into an efficient method to list-decode a class of codes which can be seen as a generalization of Reed–Solomon codes. The algorithm is specialized into a very efficient method for unique decoding. The code construction can be generalized based on algebraic-geometry codes and the decoding algorithms are generalized accordingly. Comparisons wi...
متن کاملGröbner Bases, Padé Approximation, and Decoding of Linear Codes
This paper shows how Gröbner basis techniques can be used in coding theory, especially in the construction and decoding of linear codes. A simple algorithm is given for computing the reduced Gröbner basis of the vanishing ideal of a given set of finitely many points, and it is used for finding Padé approximation of any polynomial (given implicitly), which is a major step in decoding. A new meth...
متن کاملUnderstanding Algebraic-Geometric Codes
Error-correcting codes derived from curves in an algebraic geometry are called Algebraic-Geometry Codes. The past couple of decades has seen extraordinary developments in the application of the ideas of algebraic geometry to the construction of codes and their decoding algorithms. This was initiated by the work of Goppa as generalizations of Bose-Chaudhuri-Hocquenghem (BCH), Reed-Solomon (RS), ...
متن کاملAn Algebraic Decoding Algorithm for Convolutional Codes
The class of convolutional codes generalizes the class of linear block codes in a natural way. The construction of convolutional codes which have a large free distance and which come with an e cient decoding algorithm is a major task. Contrary to the situation of linear block codes there exists only very few algebraic construction of convolutional codes. It is the purpose of this article to int...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 35 شماره
صفحات -
تاریخ انتشار 1989