Four new families of NMDS codes with dimension 4 and their applications
Yun Ding, Yang Li, Shixin Zhu · Finite Fields and Their Applications · 2024
For an [ n , k , d ] q linear code C , the singleton defect of C is defined by S ( C ) = n − k + 1 − d . When S ( C ) = S ( C ⊥ ) = 1 , the code C is called a near maximum distance separable (NMDS) code, where C ⊥ is the dual code of C . NMDS codes have important applications in finite projective geometries, designs and secret sharing schemes. In this paper, we present four new constructions of infinite families of NMDS codes with dimension 4 and completely determine their weight enumerators. As an application, we also determine the locality of the dual codes of these NMDS codes and obtain four families of distance-optimal and dimension-optimal locally recoverable codes.