Correcting ability and bounds of matroid codes

Linear block codewords consist of information and control parts. Absences of such sharing (division) are distinctive particularities of matroid codes. In this case, any k symbols from n of the received codeword can be used to restore the original sequence. New results in matroid (M-)code parameters are presented in this work. We establish the dependences of the codeword length n from parameters t and k. Lower and upper bounds of M-code existences over the field GF^k(2^m) for t and k fixed are found.