MacDonald codes over the ring F3+ vF3

Abstract

The binary MacDonald codes were introduced in [9] and q− ary version (q≥ 2) MacDonald code over the finite field Fq was studied in [10]. In [5], CJ Colbourn and M. Gupta obtained two families of MacDonald codes over the ring Z4 from Z4-simplex codes of types α and β, Sα k and S β k . They studied some fundamental properties of the codes. In [1], it was shown that the results of [5] concerning the codes over the ring Z4 are valid for the ring F2+ uF2 where u2= 0 and F2 is a field of two elements. In [2], the Mac-Donald codes over the ring F2+ uF2+ u2F2 were constructed, where u3= 0 and F2={0, 1} by using simplex codes over the ring F2+ uF2+ u2F2. Their properties were described. In [6], the MacDonald codes over F2+ vF2 were