Over the past few years, the codes Cn-1(n, q) arising from the incidence of points and hyperplanes in the projective space PG(n, q) attracted a lot of attention. In particular, small weight codewords of Cn-1(n, q) are a topic of investigation. The main result of this work states that, if q is large enough and not prime, a codeword having weight smaller than roughly 1/2(n-2)q(n-1) root q can be written as a linear combination of a few hyperplanes. Consequently, we use this result to provide a graph-theoretical sufficient condition for these codewords of small weight to be minimal.
MINIMAL CODEWORDS ARISING FROM THE INCIDENCE OF POINTS AND HYPERPLANES IN PROJECTIVE SPACES
Bartoli, D;
2021
Abstract
Over the past few years, the codes Cn-1(n, q) arising from the incidence of points and hyperplanes in the projective space PG(n, q) attracted a lot of attention. In particular, small weight codewords of Cn-1(n, q) are a topic of investigation. The main result of this work states that, if q is large enough and not prime, a codeword having weight smaller than roughly 1/2(n-2)q(n-1) root q can be written as a linear combination of a few hyperplanes. Consequently, we use this result to provide a graph-theoretical sufficient condition for these codewords of small weight to be minimal.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.