Small weight codewords of projective geometric codes

Small weight codewords in the codes arising from Desarguesian projective planes

We study codewords of small weight in the codes arising from Desarguesian projective planes. We first of all improve the results of K. Chouinard on codewords of small weight in the codes arising from PG(2, p), p prime. Chouinard characterized all the codewords up to weight 2p in these codes. Using a particular basis for this code, described by Moorhouse, we characterize all the codewords of wei...

On the geometry of small weight codewords of dual algebraic geometric codes

We investigate the geometry of the support of small weight codewords of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In particular, by restricting ourselves to the case of Hermitian codes, we recover and extend previous results obtained by the second named author joint with Marco Pellegrini and Massimiliano ...

Cyclic Codes: Low-Weight Codewords and Locators

Remarks on low weight codewords of generalized affine and projective Reed-Muller codes

A brief survey on low weight codewords of generalized Reed-Muller codes and projective generalized Reed-Muller codes is presented. In the affine case some information about the words that reach the second distance is given. Moreover the second weight of the projective Reed-Muller codes is estimated, namely a lower bound and an upper bound of this weight are given.

On Low Weight Codewords of Generalized Affine and Projective Reed - Muller Codes ( Extended abstract )

We propose new results on low weight codewords of affine and projective generalized Reed-Muller codes. In the affine case we give some results on codewords that cannot reach the second weight also called the next to minimal distance. In the projective case the second distance of generalized Reed-Muller codes is estimated, namely a lower bound and an upper bound of this weight are given.