Abstract
Several open questions in coding theory relate to non- existence or construction of certain optimal codes. Many previous problems of this kind have been solved by studying possible weight enumerators. A couple of authors in this decade have proposed using higher weights (generalised Hamming weights) to a similar effect. In this paper we suggest one approach based on the weight hierarchy, and it allows us to conduct an extremely rapid computer search to prove that there are exactly two inequivalent [36,8,16] codes. The technique can also be used to gain new information about the weight hierarchy of the putative [72,36,16] code, but not yet enough to say if it exists or not.
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Schaathun, H.G. (2009). On Higher Weights and Code Existence. In: Parker, M.G. (eds) Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10868-6_4
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DOI: https://doi.org/10.1007/978-3-642-10868-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10867-9
Online ISBN: 978-3-642-10868-6
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