M. D. S. codes and arcs in projective spaces: a survey
Abstract
Let C be a code of length k over an alphabet A of size q greather or equal 2. Having chosen m with 2 m k we impose the following condition on C: no two words agree in as many as m positions. It then follows that |C| qm. If |C|=qm, then C is called a Maximum Distance Separable code (M.D.S. code). A k-arc in PG(n,q) is a set K of k points with k at least n+1 such that no n+1 points lie in a hyperplane. It can be shown that arcs and linear M.D.S. codes are equivalent objects. Here we give a survey of important results on k-arcs, in particular we survey the answers to three fundamental problems on arcs posed by B. Segre in 1955.
Downloads
Published
Issue
Section
License
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
