An Introduction to Algebraic Geometry codes
نویسندگان
چکیده
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
منابع مشابه
Understanding 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 کاملEfficiently repairing algebraic geometry codes
Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable (MDS for short) codes. Thus, the number of nodes is upper bounded by 2, where b is the bits of data stored in each node. From both theoretical and practical points of view (see the details in Section 1), it is natural to consider regenerating codes that nearly have minimum s...
متن کاملCodes from Algebraic Number Fields
INTRODUCTION The geometry of numbers, coding theory, the Riemann hypothesis the list of key words for this lecture can be read äs a partial history of the Stichting Mathematisch Centrum. The lecture itself attempts to reflect the spirit of the SMC by displaying a new connection between these subjects. Using ideas from the geometry of numbers one can construct a class of codes from algebraic num...
متن کاملUsing concatenated algebraic geometry codes in channel polarization
Polar codes were introduced by Arikan [1] in 2008 and are the first family of error-correcting codes achieving the symmetric capacity of an arbitrary binary-input discrete memoryless channel under low complexity encoding and using an efficient successive cancellation decoding strategy. Recently, non-binary polar codes have been studied, in which one can use different algebraic geometry codes to...
متن کاملGoppa goemetry codes via elementary methods (In Portuguese)
The central objective of this dissertation was to present the Goppa Geometry Codes via elementary methods which were introduced by J.H. van Lint, R.Pellikaan and T. Høhold about 1998. On the first part of such dissertation are presented the fundamental concepts about fields of rational functions of an algebraic curve in the direction as to define the Goppa Codes on a classical manner. In this s...
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:
- CoRR
دوره abs/1505.03020 شماره
صفحات -
تاریخ انتشار 2015