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Left MQQs whose left parastrophe is also quadratic

Simona Samardjiska, Danilo Gligoroski (2012)

Commentationes Mathematicae Universitatis Carolinae

A left quasigroup ( Q , q ) of order 2 w that can be represented as a vector of Boolean functions of degree 2 is called a left multivariate quadratic quasigroup (LMQQ). For a given LMQQ there exists a left parastrophe operation q defined by: q ( u , v ) = w q ( u , w ) = v that also defines a left multivariate quasigroup. However, in general, ( Q , q ) is not quadratic. Even more, representing it in a symbolic form may require exponential time and space. In this work we investigate the problem of finding a subclass of LMQQs whose left parastrophe...

Linear spans of optimal sets of frequency hopping sequences

Gao Juntao, Hu Yupu, Li Xuelian (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Frequency hopping sequences sets are required in frequency hopping code division multiple access systems. For the anti-jamming purpose, frequency hopping sequences are required to have a large linear span. In this paper, by using a permutation polynomial δ(x) over a finite field, we transform several optimal sets of frequency hopping sequences with small linear span into ones with large linear span. The exact values of the linear span are presented by using the methods of counting the terms of the...

Linear spans of optimal sets of frequency hopping sequences∗

Gao Juntao, Hu Yupu, Li Xuelian (2012)

RAIRO - Theoretical Informatics and Applications

Frequency hopping sequences sets are required in frequency hopping code division multiple access systems. For the anti-jamming purpose, frequency hopping sequences are required to have a large linear span. In this paper, by using a permutation polynomial δ(x) over a finite field, we transform several optimal sets of frequency hopping sequences with small linear span into ones with large linear span. The exact values of the linear span are presented by using the methods of counting the terms of the...

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