The missing evaluation codes from order domain theory

Henning Ejnar Andersen, Olav Geil

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Abstract

The Feng-Rao bound gives a lower bound on the minimum distance of codes defined by means of their parity check matrices. From the Feng-Rao bound it is clear how to improve a large family of codes by leaving out certain rows in their parity check matrices. In this paper we derive a simple lower bound on the minimum distance of codes defined by means of their generator matrices. From our bound it is clear how to improve a large family of codes by adding certain rows to their generator matrices. Actually our result not only deals with the minimum distance but gives lower bounds on any generalized Hamming weight. We interpret our methods into the setting of order domain theory. In this way we fill in an obvious gap in the theory of order domains. The improved codes from the present paper are not in general equal to the Feng-Rao improved codes but the constructions are very much related.
Original languageEnglish
Place of PublicationAalborg
PublisherDepartment of Mathematical Sciences, Aalborg University
Number of pages18
Publication statusPublished - 2004
SeriesResearch Report Series
NumberR-2004-17
ISSN1399-2503

Keywords

  • Affine variety
  • evaluation code
  • Feng-Rao bound
  • generalized Hamming weight
  • geometric Goppa code
  • order domains

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