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Non-degenerate Linear Codes Determined by their Weight Enumerators

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

 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.

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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

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Kato, T. Non-degenerate Linear Codes Determined by their Weight Enumerators. AAECC 13, 475–484 (2003). https://doi.org/10.1007/s00200-002-0111-3

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  • DOI: https://doi.org/10.1007/s00200-002-0111-3

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