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An infinite class of counterexamples to a conjecture concerning nonlinear resilient functions

โœ Scribed by D. R. Stinson; J. L. Massey

Publisher
Springer
Year
1995
Tongue
English
Weight
360 KB
Volume
8
Category
Article
ISSN
0933-2790

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โœฆ Synopsis

The main construction for resilient functions uses linear errorcorrecting codes; a resilient function constructed in this way is said to be linear. It has been conjectured that if a resilient function exists, then a linear function with the same parameters exists. In this note we construct infinite classes of nonlinear resilient functions from the Kerdock and Preparata codes. We also show that linear resilient functions having the same parameters as the functions that we construct from the Kerdock codes do not exist. Thus, the aforementioned conjecture is disproved.

๐Ÿ“œ SIMILAR VOLUMES

A Counterexample to Perret's Conjecture
A Counterexample to Perret's Conjecture on Infinite Class Field Towers for Global Function Fields
โœ Harald Niederreiter; Chaoping Xing ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 92 KB

We show by a counterexample that Perret's conjecture on in"nite class "eld towers for global function "elds is wrong, and so Perret's method of in"nite rami"ed class "eld towers in the asymptotic theory of global function "elds with many rational places breaks down.