A construction of q-ary linear codes with irreducible cyclic codes

Abstract

Linear codes are an important class of error-correcting codes and widely used in secret sharing schemes, combinational designs, authentication codes and so on. The objective of this paper is to construct q-ary linear codes with good parameters from irreducible cyclic codes. Several classes of linear codes with a few weights including infinite families of distance-optimal ones are derived. The nonzero codewords of some of the codes in this paper have minimal support for inclusion and such codes can be used to construct secret sharing schemes with interesting access structures.