<PAGE>

                                                                    EXHIBIT 31.1

                                 CERTIFICATION

I, Robert R. Bennett, certify that:

     1. I have reviewed this annual report on Form 10-K of Liberty Media
Corporation;

     2. Based on my knowledge, this annual report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements made, in light of the circumstances under which such statements
were made, not misleading with respect to the period covered by this annual
report;

     3. Based on my knowledge, the financial statements and other financial
information included in this annual report fairly present in all material
respects the financial condition, results of operations and cash flows of the
registrant as of, and for, the periods presented in this annual report;

     4. The registrant's other certifying officers and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and we have:

          a) designed such disclosure controls and procedures, or caused such
     disclosure controls and procedures to be designed under our supervision, to
     ensure that material information relating to the registrant, including its
     consolidated subsidiaries, is made known to us by others within those
     entities, particularly during the period in which this annual report is
     being prepared;

          b) evaluated the effectiveness of the registrant's disclosure controls
     and procedures and presented in this annual report our conclusions about
     the effectiveness of the disclosure controls and procedures as of the end
     of the period covered by this annual report based on such evaluation; and

          c) disclosed in this annual report any change in the registrant's
     internal control over financial reporting that occurred during the
     registrant's most recent fiscal quarter (the registrant's fourth fiscal
     quarter in the case of an annual report) that has materially affected, or
     is reasonably likely to materially affect, the registrant's internal
     control over financial reporting; and

     5. The registrant's other certifying officers and I have disclosed, based
on our most recent evaluation of internal control over financial reporting, to
the registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent function):

          a) all significant deficiencies and material weaknesses in the design
     or operation of internal control over financial reporting which are
     reasonably likely to adversely affect the registrant's ability to record,
     process, summarize and report financial information; and

          b) any fraud, whether or not material, that involves management or
     other employees who have a significant role in the registrant's internal
     control over financial reporting.

                                                 /s/ ROBERT R. BENNETT
                                          --------------------------------------
                                                    Robert R. Bennett
                                          President and Chief Executive Officer

Date: March 15, 2004