On new quaternary Reed-Muller codes

Additive (Plotkin type) constructions are considered and used to obtain new families of additive codes. Applying these constructions new families of quaternary Reed-Muller codes are presented such that after using the Gray map the obtained codes have the same parameters as the classical binary linear Reed-Muller codes. To make more evident the duality relationships in the constructed families the concept of Kronecker inner product is introduced.