We show how to onstru t pseudo-random permutations that satisfy a ertain y le restri tion, for example that the permutation be y li ( onsisting of one y le ontaining all the elements) or an involution (a self-inverse permutation) with no xed points. The onstru tion an be based on any (unrestri ted) pseudo-random permutation. The resulting permutations are de ned su in tly and their evaluation a...

Lauren Williams (joint work with Einar Steingrímsson) We introduce and study a class of tableaux which we call permutation tableaux; these tableaux are naturally in bijection with permutations, and they are a distinguished subset of the " Le-diagrams " of Alex Postnikov. The structure of these tableaux is in some ways more transparent than the structure of permutations; therefore we believe tha...

We consider the function m[k](q) that counts the number of cycle permutations of a finite field Fq of fixed length k such that their permutation polynomial has the smallest possible degree. We prove the upper–bound m[k](q) ≤ (k−1)!(q(q−1))/k for char(Fq) > e(k−3)/e and the lower–bound m[k](q) ≥ φ(k)(q(q−1))/k for q ≡ 1 (mod k). This is done by establishing a connection with the Fq–solutions of ...

Let H be a subgroup of the multiplicative group of a finite field. In this note we give a method for constructing permutation polynomials over the field using a bijective map from H to a coset of H. A similar, but inequivalent, method for lifting permutation behaviour of a polynomial to an extension field is also given.

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

In this paper we solve an arbitrary matrix Riemann-Hilbert (inverse monodromy) problem with quasi-permutation monodromy representations outside of a divisor in the space of monodromy data. This divisor is characterized in terms of the theta-divisor on the Jacobi manifold of an auxiliary compact Riemann surface realized as an appropriate branched covering of CP 1 . The solution is given in terms...

Hardware implementation of partially-parallel Low-Density Parity-Check (LDPC) decoders using unstructured random matrices is very complex and requires huge hardware resources. To alleviate the complexity and minimize resource requirements, structured LDPC matrices are used. This paper presents a novel technique for constructing a multi-level Hierarchical Quasi-Cyclic (HQC) structured matrix for...

—High-speed, high-reliability requirements and strict power limitation of near-earth communications yield that the channel coding must have high coding gain and lower error floor. In this paper, an irregular quasi-cyclic low-density paritycheck (QC-LDPC) code for specific use in near-earth communications is proposed. In order to eliminate the impact of short-cycles and further improve the perf...

Previous Track Record Robert Brignall (PI) has been a Lecturer in Combinatorics at The Open University since 2010. He received his PhD in 2007 from the University of St Andrews, and from 2007–2010 he was a Heilbronn Research Fellow at The University of Bristol. In Bristol, he spent 50% of his time on classified research directed by the Heilbronn Institute, and 50% on his own research agenda. He...