A Proof of a Conjecture About a Class of Near Maximum Distance Separable Codes

Abstract

In this paper, we completely determine the number of solutions to ${\mathrm{Tr}}_q^{q^2}(bx+b)+c=0,x\in {\mu }_{q+1}\backslash \{-1\}$ for all $b\in {\mathbb{F}}_{q^2},c\in {\mathbb{F}}_q$. As an application, we can give the weight distributions of a class of linear codes, and give a completely answer to a recent conjecture about a class of NMDS codes proposed by Heng.

15 pages