Fast Decoding of Multipoint Codes from Algebraic Curves

Multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions, which have multiple poles and/or zeros on an algebraic curve. Thus, they are more general than one-point codes, which are an important class of algebraic geometry codes in the sense that they can be deco...

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Veröffentlicht in:IEEE Transactions on Information Theory Jg. 60; H. 4; S. 2054 - 2064
Hauptverfasser: Sakata, Shojiro, Fujisawa, Masaya
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.04.2014
Institute of Electrical and Electronics Engineers (IEEE)
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algebra
algebraic curve
Algebraic geometry codes
Algorithm design and analysis
Algorithms
Applied sciences
Arrays
Coding, codes
Computational complexity
Decoding
Exact sciences and technology
fast decoding
Geometry
Information theory
Information, signal and communications theory
Mathematical functions
multipoint code
one-point code
Polynomials
Signal and communications theory
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
vectorial BMS algorithm
Vectors
multipoint code
vectorial BMS algorithm
Finite field
Hermite interpolation
Algebraic code
Berlekamp Massey algorithm
Algebraic geometry codes
Decoding
algebraic curve
Data broadcast
Information dissemination
Multicast
fast decoding
Algebraic geometry
Poles and zeros
one-point code
ISSN:0018-9448, 1557-9654
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Beschreibung
Zusammenfassung:Multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions, which have multiple poles and/or zeros on an algebraic curve. Thus, they are more general than one-point codes, which are an important class of algebraic geometry codes in the sense that they can be decoded efficiently using the Berlekamp-Massey-Sakata algorithm. We present a fast method for decoding multipoint codes from a plane curve, particularly a Hermitian curve. Our method with some adaptation can be applied to decode multipoint codes from a general algebraic curve embedded in the N-dimensional affine space Fq N over a finite field F q , so that those algebraic geometry codes can be decoded efficiently if the dimension N of the affine space, including the defining curve is small.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2300473