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- Samuel J. Lomonaco, Louis H. Kauffman
- Quantum Information Processing
- 2008

In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction ofâ€¦ (More)

This paper is an introduction to relationships between topology, quantum computing and the properties of fermions. In particular we study the remarkable unitary braid group representations associatedâ€¦ (More)

- Roberta Evans Sabin, Samuel J. Lomonaco
- Applicable Algebra in Engineering, Communicationâ€¦
- 1995

Error-correcting codes which are ideals in group rings where the underlying group is metacyclic and non-abelian are examined. Such a groupG(M, N,R) is the extension of a finite cyclic group â„¤M by aâ€¦ (More)

- Samuel J. Lomonaco
- Cryptologia
- 1999

The recent application of the principles of quantum mechanics to cryptography has led to a remarkable new dimension in secret communication. As a result of these new developments, it is now possibleâ€¦ (More)

In this paper we take a totally different approach via Reidemeister homotopy chains, which gives a simpler and more natural proof enabling us to visualize geometrically the free derivatives. Brieflyâ€¦ (More)

Eilenberg-Mac Lane complexes are generalized to GEM complexes. This generalization is then shown to unify many diverse seemingly unrelated concepts in low-dimensional topology. All 2-dimensionalâ€¦ (More)

- Jonathan L. Gross, Samuel J. Lomonaco
- Journal of Graph Theory
- 1980

Kronecker studied a class of groups (p, p 1, r) , whose commutator subgroups are prime cyclic of order p, and whose commutator quotient groups are cyclic of order p 1. These are now commonly calledâ€¦ (More)

- John H. Conway, Samuel J. Lomonaco, N. J. A. Sloane
- Discrete Mathematics
- 1990

A record binary code of length 45, dimension 13 and minimal distance 16 is constructed in several ways: as an Abelian code (an ideal in the regular representation of C 3 Ã— C 15), from a [15, 6, 8]â€¦ (More)

Let (S*, k(S2)) be a knot formed by spinning a polyhedral arc a. about the standard 2-sphere S" in the 3-sphere S3. Then the second homotopy group of S"â€”k(S2) as a Z^-module is isomorphic to each ofâ€¦ (More)

- Louis H. Kauffman, Samuel J. Lomonaco
- Quantum Information Processing
- 2018

This paper is an introduction to relationships between topology, quantum computing, and the properties of Fermions. In particular, we study the remarkable unitary braid group representationsâ€¦ (More)