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 ) constructed a codeword of weight 3p−3 that is not the linear combination of three lines. We characterise their example.
- Linear codes
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics