Non-degenerate Linear Codes Determined by their Weight Enumerators

 In 1], Homma-Kim-Yoo showed that a code C such that the support of the associated projective system is a union of two linear subspaces, is uniquely determined up to equivalence by its weight enumerator. Let W _C (z) be the weight enumerator of a code C. Assuming certain conditions on the coefficients of W _C (z) for some range, we prove that the support of the associated projective system is a union of two linear subspaces. Received: February 27, 2002; revised version: October 2, 2002 Keywords: Linear code, Projective system, Weight enumerator. MSC2000: 94B27, 94B65, 51E20 Partially supported by Grant-in-Aid for Scientific Research, Ministry of Education, #12640180