Abstract
Conway and Pless have enumerated in [6] the 85 non-equivalent self-dual doubly-even codes of length 32. From this enumeration it happened that five codes were extremal, having the largest possible minimum distance which is 8 in length 32. Two of these five codes were already known, the second order Reed-Muller code RM32 and the extended quadratic residue code QR32 of length 32. The other three denoted 2g 16, 8f 4 and 16f 2 by Conway and Pless were new. In [8], Koch has given another more direct construction of these Conway-Pless codes denoted by him F = 2g 16, U = 8f 4 and G = 16f 2. Since the five extremal codes, though pairwise non-equivalent, have the same weight enumerator it is natural to try to calculate the coset weight enumerators and to ask for some parameters which may distinguish them.
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© 1993 Springer-Verlag Wien
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Camion, P., Courteau, B., Monpetit, A. (1993). Coset Weight Enumerators of the Extremal Self-Dual Binary Codes of Length 32. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_2
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DOI: https://doi.org/10.1007/978-3-7091-2786-5_2
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