Orthogonal quadruple systems and 3-frames

Authors:
William B. Muse;K. T. Phelps
Affiliations:
Discrete & Statistical Sciences, Auburn University, Auburn, AL;Discrete & Statistical Sciences, Auburn University, Auburn, AL
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

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Abstract

Orthogonal quadruple systems are defined and investigated. Orthogonal quadruple systems with an additional nesting property are shown to provide a new construction of 3-frames F(3,4, n{2}) (Design Codes Cryptogr. 4 (1994) 5). Constructions for pairs of nested orthogonal quadruple systems are provided. Applications to 2-resolvable Steiner quadruple systems and highly nonlinear functions are discussed.