Are 2-weight projective cyclic codes irreducible?
We prove the following result on a 2-weight projective cyclic code C over F-q. If q = 2 then C is irreducible. If q not equal 2 then either C is irreducible or C is the direct sum of two 1-weight irreducible cyclic codes.
2-weight projective cyclic codes cyclic codes irreducible cyclic codes