Near MDS codes from oval polynomials

A linear code with parameters of the form [n,k,n?k+1] is referred to as an MDS (maximum distance separable) code. [n,k,n?k] said be almost (i.e., maximum or AMDS for short. near separable (in short, NMDS) if both and its dual are separable. Near codes correspond interesting objects in finite geometry have nice applications combinatorics cryptography. There many unsolved problems about codes. It hard construct infinite family whose weight distributions can settled. In this paper, seven families [2m+1,3,2m?2] over GF(2m) [2m+2,3,2m?1] constructed special oval polynomials odd m. addition, nine optimal [2m+3,3,2m] general. The these