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10 items by relevance
1 Journal article

Algebraic-Geometry Codes

Høholdt, Tom; Blake, Ian; Heegaard, Chris; Wei, Victor

I E E E Transactions on Information Theory — 1998, Volume 44, Issue 6, pp. 2596-2618

The theory of error-correcting codes derived from curves in an algebraic geometry was initiated by the work of Goppa as generalizations of Bose-Chaudhuri-Hocquenghem (BCH), Reed-Solomon (RS), and Goppa codes. The development of the theory has received intense consideration since that time

Year: 1998

Language: English

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2 Journal article

Performance analysis of a decoding algorithm for algebraic-geometry codes

Høholdt, Tom; Jensen, Helge Elbrønd; Nielsen, Rasmus Refslund

I E E E Transactions on Information Theory — 1999, Volume 45, Issue 5, pp. 1712-1717

The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out

Year: 1999

Language: English

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3 Journal article

Construction and decoding of a class of algebraic geometry codes

Justesen, Jørn; Larsen, Knud J.; Jensen, Helge Elbrønd; Havemose, Allan; Høholdt, Tom

I E E E Transactions on Information Theory — 1989, Volume 35, Issue 4, pp. 811-821

A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result

Year: 1989

Language: English

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4 Journal article · Conference paper

Fast Erasure-and error decoding of algebraic geometry codes up to the Feng-Rao bound

Høholdt, Tom; Jensen, Helge Elbrønd; Sakata, Shojiro; Leonard, Doug

I E E E Transactions on Information Theory — 1998, Volume 44, Issue 4, pp. 1558-1564

This correspondence gives an errata (that is erasure-and error-) decoding algorithm of one-point algebraic-geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-Massey algorithm and the voting procedure of Feng and Rao.

Year: 1998

Language: English

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