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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1534375
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