On optimal and proper binary codes from irreducible cyclic codes over GF(2~m)

摘要

We prove that binary images of irreducible cyclic codes C overGF(2~m)and binary concatenated codes of C and a binary[m +1, m,2]even-parity code are optimal(in The sense that they meet theGriesmer bound with equality)and Proper, if a root of the checkpolynomial of C is primitive over GF(2~m)or its extensions.