Abstract
In this chapter we prove two of the most remarkable results in all of coding theory. The first, due to Mrs. F.J. MacWilliams, says that the weigth enumeration of the dual code C┴ is completely determined just by the weight enumerator of C. The second result, due to A.M. Gleason, states that the weight enumerator of any self-dual code (in which the weigth of any codeword is a multiple of 4) is a polynomial in the weigth enumerators of the extended Hamming code and the extended Golay code. This is an extremely powerful theorem for finding the minimum distance of large self-dual codes. It can also be used to show that certain codes do not exist.
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© 1975 Springer-Verlag Wien
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Sloane, N.J.A. (1975). The Theorems of MacWilliams and Gleason. In: A Short Course on Error Correcting Codes. International Centre for Mechanical Sciences, vol 188. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2864-0_4
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DOI: https://doi.org/10.1007/978-3-7091-2864-0_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81303-4
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