Direct sums of balanced functions, perfect nonlinear functions, and orthogonal cocycles

✍ Scribed by Alain LeBel; K. J. Horadam

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 138 KB
• Volume: 16
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20187

✦ Synopsis

Abstract

Determining if a direct sum of functions inherits nonlinearity properties from its direct summands is a subtle problem. Here, we correct a statement by Nyberg on inheritance of balance and we use a connection between balanced derivatives and orthogonal cocycles to generalize Nyberg's result to orthogonal cocycles. We obtain a new search criterion for PN functions and orthogonal cocycles mapping to non‐cyclic abelian groups and use it to find all the orthogonal cocycles over Z~2~^t^, 2 ≤ t ≤ 4. We conjecture that any orthogonal cocycle over Z~2~^t^, t ≥ 2, must be multiplicative. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 173–181, 2008