Stability of k mod p multisets and small weight codewords of the code generated by the lines of PG(2,q)

T. Szőnyi, Zsuzsa Weiner

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we prove a stability result on k mod p multisets of points in PG(2,q), q=ph. The particular case k=0 is used to describe small weight codewords of the code generated by the lines of PG(2,q), as linear combination of few lines. Earlier results proved this for codewords with weight less than 2.5q, while our result is valid until cqq. It is sharp when 27<q square and h≥4. When q is a prime, De Boeck and Vandendriessche (see [2]) constructed a codeword of weight 3p−3 that is not the linear combination of three lines. We characterise their example.

Original languageEnglish
Pages (from-to)321-333
Number of pages13
JournalJournal of Combinatorial Theory. Series A
Volume157
DOIs
Publication statusPublished - Jul 1 2018

Keywords

  • Linear codes
  • PG(2,q)
  • Stability

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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