Abstract
We begin this chapter by defining various weight enumerators that can be associated with a code, and then discuss the MacWilliams identity, which relates the weight enumerators of a code and its dual. In §2.3 we show how to describe the most important families of self-dual codes that have been studied to date as Types, using our new language of representations of form rings. Section §2.4 gives a number of important examples of self-dual codes of the different Types together with their weight enumerators.
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© 2006 Springer
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Nebe, G., Rains, E.M., Sloane, N.J. (2006). Weight Enumerators and Important Types. In: Self-Dual Codes and Invariant Theory. Algorithms and Computation in Mathematics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30731-1_2
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DOI: https://doi.org/10.1007/3-540-30731-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30729-7
Online ISBN: 978-3-540-30731-0
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