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no. 3
Quasihomomorphisms from the integers into Hamming metrics
Draisma, Jan1; Eggermont, Rob H.2; Seynnaeve, Tim3; Tairi, Nafie4; Ventura, Emanuele5
1 Mathematical Institute University of Bern Sidlerstrasse 5 3012 Bern Switzerland; and Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600MB Eindhoven the Netherlands
2 Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600MB Eindhoven the Netherlands
3 Department of Computer Science KU Leuven Celestijnenlaan 200A 3001 Leuven Belgium
4 Mathematical Institute University of Bern Alpeneggstrasse 22 3012 Bern Switzerland
5 Politecnico di Torino Dipartimento di Scienze Matematiche “G.L. Lagrange” Corso Duca degli Abruzzi 24 10129 Torino Italy
Algebraic Combinatorics, Volume 7 (2024) no. 3, pp. 843-851.

A function f:ℤ→ℚ n is a c-quasihomomorphism if the Hamming distance between f(x+y) and f(x)+f(y) is at most c for all x,y∈ℤ. We show that any c-quasihomomorphism has distance at most some constant C(c) to an actual group homomorphism; here C(c) depends only on c and not on n or f. This gives a positive answer to a special case of a question posed by Kazhdan and Ziegler.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.348
Classification: 11B30
Keywords: Quasihomomorphisms, Hamming distance, Linear approximation

Draisma, Jan 1; Eggermont, Rob H. 2; Seynnaeve, Tim 3; Tairi, Nafie 4; Ventura, Emanuele 5

1 Mathematical Institute University of Bern Sidlerstrasse 5 3012 Bern Switzerland; and Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600MB Eindhoven the Netherlands
2 Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600MB Eindhoven the Netherlands
3 Department of Computer Science KU Leuven Celestijnenlaan 200A 3001 Leuven Belgium
4 Mathematical Institute University of Bern Alpeneggstrasse 22 3012 Bern Switzerland
5 Politecnico di Torino Dipartimento di Scienze Matematiche “G.L. Lagrange” Corso Duca degli Abruzzi 24 10129 Torino Italy
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Quasihomomorphisms from the integers into {Hamming} metrics},
     journal = {Algebraic Combinatorics},
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Draisma, Jan; Eggermont, Rob H.; Seynnaeve, Tim; Tairi, Nafie; Ventura, Emanuele. Quasihomomorphisms from the integers into Hamming metrics. Algebraic Combinatorics, Volume 7 (2024) no. 3, pp. 843-851. doi : 10.5802/alco.348. https://alco.centre-mersenne.org/articles/10.5802/alco.348/

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