Near-MDS codes from elliptic curves

Abstract

AbstractWe provide a geometric construction of $$[n,9,n-9]_q$$ [ n , 9 , n - 9 ] q near-MDS codes arising from elliptic curves with n$${\mathbb {F}}_q$$ F q -rational points. Furthermore, we show that in some cases these codes cannot be extended to longer near-MDS codes.