On semigroups generated by two consecutive integers and improved Hermitian codes

Maria Bras-Amorós, Michael E. O'Sullivan

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

Analysis of the Berlekamp-Massey-Sakata algorithm for decoding one-point codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm. The second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic. In this work, formulae are given for the redundancies of Hermitian codes optimized with respect to these criteria as well as the formula for the order bound on the minimum distance. The results proceed from an analysis of numerical semigroups generated by two consecutive integers. © 2007 IEEE.
Original languageEnglish
Pages (from-to)2560-2566
JournalIEEE Transactions on Information Theory
Volume53
Issue number7
DOIs
Publication statusPublished - 1 Jul 2007

Keywords

  • Feng-Rao improved code
  • Hermitian curve
  • Numerical semigroup

Fingerprint Dive into the research topics of 'On semigroups generated by two consecutive integers and improved Hermitian codes'. Together they form a unique fingerprint.

Cite this