Classification of the odd sets in \(\hbox {PG}(4,4)\) and its application to coding theory
A set \({\fancyscript{K}}\) in \(\hbox {PG}(r,4), r \ge 2\), is odd if every line meets \({\fancyscript{K}}\) in an odd number of points. We show there are exactly 45 inequivalent odd sets in \(\hbox {PG}(4,4)\) up to projective equivalence. As an application to coding theory, a new sufficient condition for the extendability of quaternary linear codes is given.
odd sets extendability of linear codes projective geometry 94b05 94b27