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On the delsarte-goethals codes and their formal duals

✍ Scribed by Ferdinand B. Hergert

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
872 KB
Volume
83
Category
Article
ISSN
0012-365X

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✦ Synopsis

Exploiting properties of association schemes arising from quotient spaces of nested linear codes having the same automorphism group, we show how the the nonlinear Delsarte-Goethals codes can be used to construct their formal duals. This yields a unified construction for these two families of nonlinear codes.

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## Abstract For Ξ© an open subset of IR^N^ and 1 < __p__ < ∞, we prove that any complemented subspace __E__ of __L__^p^~loc~ (Ξ©) contains either a complemented copy of (__l__^2^)^IN^ or a complemented copy of (__l__^p^)^IN^, provided β‰ˆοΈ __F__ β‰ˆοΈ and Ο‰ and β‰ˆοΈ Ο‰βŠ• __F__ with __F__ Banach space. We also