On the subfield subcodes of Hermitian codes

Fernando Pinero, Heeralal Janwa

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.
Original languageEnglish
JournalDesigns, Codes and Cryptography
Volume70
Issue number1-2
Pages (from-to)157-173
ISSN0925-1022
DOIs
Publication statusPublished - 2014

Keywords

  • Subfield subcodes
  • Hermitian codes
  • Algebraic geometry codes
  • Gröbner basis
  • Decoding subfield subcodes
  • List-decoding of subfield subcodes

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